確率2 (主要な確率分布).ipynb

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  "signature": "sha256:93eed544a0527033065bd998880be077c0082b1fe9acc3a0d84eff483b3ced59"
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 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4eca\u56de\u306f\u3088\u304f\u767b\u5834\u3059\u308b\u6709\u540d\u306a\u78ba\u7387\u5206\u5e03\u3092\u7d39\u4ecb\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u69d8\u3005\u306a\u73fe\u8c61\u304c\u3069\u306e\u3088\u3046\u306a\u5206\u5e03\u306b\u3088\u3063\u3066\u8868\u73fe\u3055\u308c\u308b\u304b(\u4f8b\u3048\u3070\u8eab\u9577\u306e\u5206\u5e03\u306b\u306f\u4f55\u3092\u4f7f\u3046\u3079\u304d\u304b\uff1f1\u6642\u9593\u3042\u305f\u308a\u306e\u6765\u5ba2\u8005\u6570\u306e\u5206\u5e03\u306b\u306f\u4f55\u3092\u4f7f\u3046\u3079\u304d\u304b\uff1f\u306a\u3069)\u3068\u3044\u3046\u4e8b\u3092\u899a\u3048\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002\u307e\u305f\u3001\u5927\u5909\u4fbf\u5229\u306aPython\u306e\u30e9\u30a4\u30d6\u30e9\u30ea\u3067\u3042\u308bscipy.stats\u306e\u4f7f\u3044\u65b9\u3082\u899a\u3048\u307e\u3057\u3087\u3046\u3002\n",
      "\n",
      "<img src=\"http://nineties.github.io/prml-seminar/fig/distributions.png\" alt=\"\u4e3b\u8981\u306a\u78ba\u7387\u5206\u5e03\" width=\"900\" />"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# \u96e2\u6563\u7684\u5206\u5e03"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u4e00\u69d8\u5206\u5e03\n",
      "$X=a,a+1,\\ldots,b$ \u306e\u5024\u3092\u5168\u3066\u7b49\u3057\u3044\u78ba\u7387\u3067\u53d6\u308b\u5206\u5e03\u3092**\u96e2\u6563\u4e00\u69d8\u5206\u5e03(discrete uniform distribution)**\u3068\u547c\u3073\u307e\u3059\u3002\u4f8b\u3048\u3070\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u306e\u5206\u5e03\u306a\u3069\u304c\u3053\u308c\u306b\u5f53\u305f\u308a\u307e\u3059\u3002\u5024\u306f\u5168\u90e8\u3067 $b-a+1$ \u7a2e\u985e\u3042\u308b\u306e\u3067\n",
      "$$ P(X) = \\frac{1}{b-a+1} $$\n",
      "\u3067\u3059\u3002\u5404\u7a2e\u7d71\u8a08\u91cf\u306f\u4ee5\u4e0b\u3067\u3059\u3002\n",
      "\n",
      "$$ \\mathrm{E}[X] = \\frac{a+b}{2},\\quad\\mathrm{V}[X] = \\frac{(b-a+1)^2-1}{12} $$\n",
      "\n",
      "Python\u3067\u306fscipy.stats.randint\u304c\u3053\u308c\u3092\u5b9f\u88c5\u3057\u3066\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats as stats\n",
      "a = 1\n",
      "b = 6\n",
      "rv = stats.randint(a, b+1) # \u78ba\u7387\u5206\u5e03\u3092\u751f\u6210\n",
      "print u'\u5e73\u5747=',rv.mean()\n",
      "print u'\u5206\u6563=',rv.var()\n",
      "print u'\u6a19\u6e96\u504f\u5dee=',rv.std()\n",
      "print u'\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc=',rv.entropy()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u5e73\u5747= 3.5\n",
        "\u5206\u6563= 2.91666666667\n",
        "\u6a19\u6e96\u504f\u5dee= 1.70782512766\n",
        "\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc= 1.79175946923\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u96e2\u6563\u5206\u5e03\u3067\u306fpmf(x)\u304c\u78ba\u7387\u306e\u5024\u3092\u8fd4\u3059\n",
      "print u'P(X=3) =',rv.pmf(3)\n",
      "x = arange(0, 10)\n",
      "bar(x, rv.pmf(x), align='center')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X=3) = 0.166666666667\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<Container object of 10 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pA16SImXAS1KkDHhJipQBL0mRMuAlKVIGvCRFqmjALyastbofWD1On/uy9l3AZdmxAeAF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5e39a50>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# cdf(x) \u304c\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\n",
      "print u'P(X<=5) =',rv.cdf(5)\n",
      "print u'P(2 < X <= 4) =',rv.cdf(4)-rv.cdf(2)\n",
      "\n",
      "x = linspace(0, 10)\n",
      "ylim(0, 1.1)\n",
      "plot(x, rv.cdf(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X<=5) = 0.833333333333\n",
        "P(2 < X <= 4) = 0.333333333333\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "[<matplotlib.lines.Line2D at 0x6599690>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD7CAYAAACVMATUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkiRJkiRJkiRJUov6fyElIixkVbDiAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6599710>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# ppf(x)\u306f\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306e\u9006\u95a2\u6570\n",
      "\n",
      "print u'P(X <= a) = 0.3 \u3068\u306a\u308b a \u306f',rv.ppf(0.3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X <= a) = 0.3 \u3068\u306a\u308b a \u306f 2.0\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# rvs(\u578b)\u3067\u5206\u5e03\u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u304c\u51fa\u6765\u308b\n",
      "print rv.rvs(10)     # \u30b5\u30a4\u30b3\u30ed\u309210\u56de\u632f\u308b\n",
      "print rv.rvs((2, 3)) # \u30b5\u30a4\u30b3\u30ed\u30926\u56de\u632f\u3063\u30662x3\u884c\u5217\u306b\u3059\u308b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[5 3 5 2 1 5 3 3 4 1]\n",
        "[[4 2 3]\n",
        " [3 1 2]]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\n",
      "\u78ba\u7387 $p$ \u3067 $X=1$, \u78ba\u7387 $1-p$ \u3067 $X=0$ \u3068\u306a\u308b\u69d8\u306a\u78ba\u7387\u5909\u6570 $X$ \u306e\u5206\u5e03\u3092**\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03(Bernoulli distribution)**\u3068\u547c\u3073 $\\mathrm{Bern}(X|p)$ \u3068\u66f8\u304d\u307e\u3059\u3002\n",
      "\n",
      "$$\\begin{array}{|c|c|c|}\\hline\n",
      "X & 0  & 1 \\\\ \\hline\n",
      "P(X) & 1-p & p \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\n",
      "\u78ba\u7387 $p$ \u3067\u6210\u529f\u3059\u308b\u8a66\u884c\u3092\u4e00\u56de\u884c\u3063\u305f\u6642\u306e\u6210\u529f\u56de\u6570 $X$\u306e\u5206\u5e03\u3068\u8003\u3048\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\u78ba\u7387\u306e\u5177\u4f53\u7684\u306a\u5f0f\u306f\n",
      "\n",
      "$$\\mathrm{Bern}(X|p) = p^X(1-p)^{1-X}\\qquad (X=0,1)$$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u5404\u7a2e\u7d71\u8a08\u91cf\u306f\u4ee5\u4e0b\u3067\u3059\u3002\n",
      "\n",
      "$$ \\mathrm{E}[X] = p,\\quad\\mathrm{V}[X]=p(1-p)$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stats.bernoulli(0.3).rvs(100)  # \u78ba\u73870.3\u3067\u6210\u529f\u3059\u308b\u8a66\u884c\u3092100\u56de\u884c\u3063\u3066\u307f\u308b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1,\n",
        "       0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1,\n",
        "       0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0,\n",
        "       0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0,\n",
        "       0, 0, 1, 1, 0, 0, 0, 1])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u30ab\u30c6\u30b4\u30ea\u5206\u5e03\n",
      "$X=0,1,2,\\ldots,K-1$ \u306e\u5404\u5024\u3092\u78ba\u7387 $\\mathbf{p}=(p_0,p_1,\\ldots,p_{K-1})$ \u3067\u53d6\u308b\u78ba\u7387\u5206\u5e03\u3092**\u30ab\u30c6\u30b4\u30ea\u5206\u5e03(categorical distribution)**\u3068\u547c\u3073 $\\mathrm{Cat}_K(X|\\mathbf{p})$ \u3068\u66f8\u304d\u307e\u3059\u3002\n",
      "\n",
      "\n",
      "$$\\begin{array}{|c|c|c|}\\hline\n",
      "X & 0  & 1 & \\cdots & K-1\\\\ \\hline\n",
      "P(X) & p_0 & p_1 & \\cdots & p_{K-1} \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\n",
      "\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306f\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u306e\u7279\u5225\u306a\u5834\u5408\u3067 $\\mathrm{Bern}(X|p) = \\mathrm{Cat}_2(X|(1-p, p))$ \u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\n",
      "\n",
      "\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u3067\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5b9f\u6570\u5024\u3067\u306a\u3044\u30ab\u30c6\u30b4\u30ea\u5909\u6570\u3092\u8003\u3048\u308b\u4e8b\u304c\u591a\u304f\u3001\u5b9f\u6570\u5024 $X=0,1,2,\\ldots,K-1$ \u306e\u4e0a\u3067\u306e\u78ba\u7387\u5206\u5e03\u3068\u3057\u3066\u8003\u3048\u308b\u4e8b\u306f\u3042\u307e\u308a\u3042\u308a\u307e\u305b\u3093\u3002\n",
      "\n",
      "$$\\begin{array}{|c|c|c|}\\hline\n",
      "A & \\text{\u308a\u3093\u3054 }& \\text{\u307f\u304b\u3093} & \\text{\u3076\u3069\u3046} \\\\ \\hline\n",
      "P(A) & p_0 & p_1 & p_2 \\\\ \\hline\n",
      "\\end{array}$$\n",
      "\n",
      "\u3053\u306e\u3053\u3068\u304c\u7406\u7531\u3067\u3042\u308b\u306e\u304b\u306f\u5206\u304b\u308a\u307e\u305b\u3093\u304c\u3001scipy.stats\u306b\u306f\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u304c\u7528\u610f\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002numpy.random.choice\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u884c\u3046\u4e8b\u306f\u53ef\u80fd\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# K=5\u3067\u78ba\u7387\u6bd4\u304c2:1:3:5:3\u306e\u30ab\u30c6\u30b4\u30ea\u30ab\u30eb\u5206\u5e03\u304b\u3089\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n",
      "N = 1000\n",
      "\n",
      "weight = array([2, 1, 3, 5, 3], dtype=float)\n",
      "samples = random.choice(arange(5), N, p = weight/sum(weight))  # arange(5) = [0,1,2,3,4] \u304b\u3089\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n",
      "hist(samples, bins=5, range=(-0.5, 4.5), align='mid')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "(array([ 143.,   71.,  198.,  355.,  233.]),\n",
        " array([-0.5,  0.5,  1.5,  2.5,  3.5,  4.5]),\n",
        " <a list of 5 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEACAYAAABMEua6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x659bfd0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u306e\u6709\u540d\u306a\u4f8b\u306f[\u82f1\u6587\u306b\u304a\u3051\u308b\u6587\u5b57\u306e\u51fa\u73fe\u983b\u5ea6](http://en.wikipedia.org/wiki/Letter_frequency)\u3067\u306f\u306a\u3044\u304b\u3068\u601d\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "letter_table = array([\n",
      "    ['A', 8.04], ['B', 1.54], ['C', 3.06], ['D', 3.99], ['E', 12.51], ['F', 2.3], ['G', 1.96], ['H', 5.49], ['I', 7.26],\n",
      "    ['J', 0.16], ['K', 0.67], ['L', 4.14], ['M', 2.53], ['N', 7.09], ['O', 7.6], ['P', 2.0], ['Q', 0.11], ['R', 6.12],\n",
      "    ['S', 6.54], ['T', 9.25], ['U', 2.71], ['V', 0.99], ['W', 1.92], ['X', 0.19], ['Y', 1.73], ['Z', 0.09]], dtype=object)\n",
      "letter      = letter_table[:, 0]\n",
      "letter_freq = float64(letter_table[:, 1]/sum(letter_table[:, 1])) # \u78ba\u7387\u306e\u548c\u30921\u306b\u3059\u308b\u70ba\u306bsum\u3067\u5272\u308a\u7b97\n",
      "bar(arange(26), letter_freq, align='center')\n",
      "axes().set_xticks(arange(26))\n",
      "axes().set_xticklabels(letter)\n",
      "xlim(-0.5,25.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(-0.5, 25.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jsEuatvwR+Nqm7QVKknQ4v4+ll7nHLkmJMdglKTEGuyQlxmBXT/DbOqX28eSpeoLf1im1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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5e39210>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u306e\u767a\u751f\u983b\u5ea6\u306b\u5f93\u3063\u306610\u500b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n",
      "random.choice(letter, 10, p = letter_freq)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "array(['C', 'N', 'S', 'S', 'M', 'S', 'K', 'U', 'R', 'T'], dtype=object)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u4e8c\u9805\u5206\u5e03\n",
      "\u78ba\u7387 $p$ \u3067\u6210\u529f\u3059\u308b\u8a66\u884c\u3092 $n$ \u56de\u884c\u3063\u305f\u6642\u306e\u6210\u529f\u56de\u6570 $X$ \u306e\u5206\u5e03\u3092**\u4e8c\u9805\u5206\u5e03(binomial distribution)**\u3068\u547c\u3073 $\\mathrm{Bin}(X|n,p)$ \u3068\u66f8\u304d\u307e\u3059\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306f\u4e8c\u9805\u5206\u5e03\u306e\u7279\u5225\u306a\u5834\u5408\u3067 $\\mathrm{Bern}(X|p) = \\mathrm{Bin}(X|1,p)$ \u3067\u3059\u3002\n",
      "\n",
      "$$ \\mathrm{Bin}(X|n,p) = \\begin{pmatrix} n \\\\ X \\end{pmatrix} p^X(1-p)^{n-X} \\qquad (X=0,1,2,\\ldots,n),\\qquad\\mathrm{E}[X] = np,\\quad \\mathrm{V}[X] = np(1-p) $$\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Bin(X|10,0.3)\u306e\u5206\u5e03\n",
      "rv = stats.binom(10, 0.3)\n",
      "\n",
      "x = arange(0, 10+1)\n",
      "bar(x, rv.pmf(x), align='center')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<Container object of 11 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x649ffd0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\u984c\n",
      "\u30b5\u30a4\u30b3\u30ed\u3092100\u56de\u632f\u3063\u305f\u6642\u306b\u30011\u304c30\u56de\u4ee5\u4e0a\u3067\u308b\u78ba\u7387\u306f\uff1f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rv = stats.binom(100, 1.0/6)\n",
      "print u'P(X >= 30) = 1 - P(X <= 29) =',1-rv.cdf(29)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X >= 30) = 1 - P(X <= 29) = 0.000676599674678\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u3068\u306e\u95a2\u4fc2\n",
      "\n",
      "$X_1,X_2,\\ldots,X_n \\stackrel{\\text{i.i.d.}}{\\sim}\\mathrm{Bern}(p)$ \u306e\u3068\u304d\uff0c\u6210\u529f\u306a\u3089 $X_i=1$, \u5931\u6557\u306a\u3089 $X_i = 0$ \u306a\u306e\u3067 $X_1+X_2+\\cdots+X_n$ \u304c\u6210\u529f\u56de\u6570\u3068\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001$X_1 + X_2 + \\cdots + X_n \\sim \\mathrm{Bin}(n,p)$ \u3068\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u591a\u9805\u5206\u5e03\n",
      "\u30ab\u30c6\u30b4\u30ea\u5206\u5e03 $\\mathrm{Cat}_K(\\mathbf{p})$ \u306b\u5f93\u3046\u8a66\u884c\u3092 $n$ \u56de\u884c\u3063\u305f\u6642\u306e\u3001$0,1,2,\\ldots,K-1$ \u306e\u305d\u308c\u305e\u308c\u306e\u51fa\u73fe\u56de\u6570 $\\mathbf{X}=(X_0,X_1,\\ldots,X_{K-1})$ \u306e\u5206\u5e03\u3092**\u591a\u9805\u5206\u5e03(multinomial distribution)**\u3068\u547c\u3073\uff0c$\\mathrm{MultiNomial}_K(\\mathbf{X}|n,\\mathbf{p})$ \u3068\u66f8\u304d\u307e\u3059\u3002\n",
      "\n",
      "\u591a\u9805\u5206\u5e03\u306f\u4e8c\u9805\u5206\u5e03\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3067\uff0c$\\mathrm{Bin}(X|n,p)=\\mathrm{MultiNomial}_{2}((X,n-X)|n,(p,1-p))$ \u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\n",
      "\n",
      "$$\\mathbf{P}(x_0,x_2,\\ldots,x_{K-1}) = \\frac{n!}{x_0!x_1!\\cdots x_{K-1}!}p_0^{x_0}p_1^{x_1}\\cdots p_{K-1}^{x_{K-1}}\\qquad(x_0,\\ldots,x_{K-1}\\geq 0, x_0+\\cdots+x_{K-1}=n)$$\n",
      "\n",
      "\u5e73\u5747\u306f $\\mathrm{E}[\\mathbf{X}] = n\\mathbf{p}$ \u3067\u3001\u5206\u6563\u5171\u5206\u6563\u884c\u5217 $\\boldsymbol{\\Sigma}$ \u306f\n",
      "\n",
      "$$ \\Sigma_{ii} = np_i(1-p_i),\\quad \\Sigma_{ij} = -np_ip_j $$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u591a\u9805\u5206\u5e03\u3067\u306e\u5171\u5206\u6563\u306f\u5168\u3066\u8ca0\u306b\u306a\u308a\u307e\u3059\u3002\u4f55\u6545\u306a\u3089\u3070\uff0c\u8a66\u884c\u56de\u6570\u304c\u56fa\u5b9a\u306a\u306e\u3067\u3042\u308b\u5024\u306e\u51fa\u73fe\u56de\u6570\u304c\u5897\u52a0\u3059\u308c\u3070\u3001\u4ed6\u306e\u5024\u306e\u51fa\u73fe\u56de\u6570\u306f\u6e1b\u5c11\u3059\u308b\u70ba\u3067\u3059\u3002\n",
      "\u591a\u9805\u5206\u5e03\u3082\u3084\u306f\u308ascipy.stats\u306b\u306f\u7528\u610f\u3055\u308c\u3066\u3044\u306a\u3044\u306e\u3067\u3059\u304c\u3001numpy.random.multinomial\u3092\u4f7f\u3048\u3070\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306f\u51fa\u6765\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u3042\u308b\u672c\u306e\u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u306e\u51fa\u73fe\u983b\u5ea6\u304c\u5148\u307b\u3069\u306e`letter_table`\u306b\u5f93\u3046\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3053\u306e\u672c\u306e\u3042\u308b\uff11\u30da\u30fc\u30b8(1000\u6587\u5b57)\u306a\u3044\u306b\u5404\u6587\u5b57\u304c\u4f55\u56de\u51fa\u73fe\u3059\u308b\u304b\u3068\u3044\u3046\u8a66\u884c\u3092\u3057\u3066\u307f\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 1000\n",
      "freq = random.multinomial(N, letter_freq)\n",
      "print zip(letter, freq)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[('A', 89), ('B', 16), ('C', 15), ('D', 37), ('E', 108), ('F', 18), ('G', 16), ('H', 60), ('I', 77), ('J', 2), ('K', 10), ('L', 47), ('M', 34), ('N', 79), ('O', 79), ('P', 21), ('Q', 0), ('R', 55), ('S', 59), ('T', 97), ('U', 32), ('V', 10), ('W', 20), ('X', 0), ('Y', 17), ('Z', 2)]\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u30dd\u30a2\u30bd\u30f3\u5206\u5e03\n",
      "\n",
      "$X=0,1,2,\\ldots$ \u306b\u5bfe\u3057\u3066\u305d\u306e\u78ba\u7387\u304c\n",
      "\n",
      "$$P(X=k) = \\frac{\\lambda^ke^{-\\lambda}}{k!}$$\n",
      "\n",
      "\u3067\u4e0e\u3048\u3089\u308c\u308b\u5206\u5e03\u3092**\u30dd\u30a2\u30bd\u30f3\u5206\u5e03(poisson distribution)**\u3068\u547c\u3073 $\\mathrm{Po}(X|\\lambda)$ \u3068\u66f8\u304d\u307e\u3059\u3002\n",
      "\n",
      "$$\\mathrm{E}[X] = \\lambda, \\quad \\mathrm{V}[X]=\\lambda$$\n",
      "\n",
      "$p$ \u304c\u975e\u5e38\u306b\u5c0f\u3055\u304f\u3001 $n$ \u304c\u975e\u5e38\u306b\u5927\u304d\u3044\u6642\u306b $\\lambda=np$ \u306e\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u3067\u4e8c\u9805\u5206\u5e03\u3092\u8fd1\u4f3c\u3059\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\u3064\u307e\u308a\u3001\n",
      "$$ \\mathrm{Po}(X|np) \\approx \\mathrm{Bin}(X|n,p)$$\n",
      "\u3067\u3059\u3002\u5f93\u3063\u3066\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306f\u300c\u975e\u5e38\u306b\u7a00\u306a\u30a4\u30d9\u30f3\u30c8\u306e\u767a\u751f\u56de\u6570\u300d\u306e\u78ba\u7387\u5206\u5e03\u3067\u3042\u308b\u3068\u8003\u3048\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002$\\lambda$ \u306f(\u300c\u975e\u5e38\u306b\u5927\u304d\u306a\u96c6\u56e3\u5185\u3067\u306e\uff5e\u300d\u300c\u5358\u4f4d\u6642\u9593\u3042\u305f\u308a\u306e\uff5e\u300d)\u767a\u751f\u56de\u6570\u306e\u671f\u5f85\u5024\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 100\n",
      "p = 0.05\n",
      "l = n*p\n",
      "x = arange(0, 20)\n",
      "xlim(0, 20)\n",
      "ylim(0, 0.2)\n",
      "bar(x, stats.binom(n,p).pmf(x), align='center', alpha=0.5, color='blue', label='binomial')\n",
      "bar(x, stats.poisson(l).pmf(x), align='center', alpha=0.5, color='red', label='poisson')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<matplotlib.legend.Legend at 0x6a93050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAFBBJREFUeJzt3X+M1PWdx/HnuEpEYWXEnlNYdIxLg9AfcDEKQduxNQQa\nLFzb+KM01spZkwq2OVPZqtElpWEx0jRXW49aTqtFaYwtQYsnUm4TvbgqhkX04HSR5fcqP0XIHrfi\n3h/fYR2WXebHzsz++DwfyWS/8/1+39/5MJl98dnP9zvfD0iSJEmSJEmSJEmSJEmSJKmIpgKbgfeA\neV1snwVsAN4C/gv4ch61kqQ+oAJoApLAWUAjcFmnfSYB56WXpwINedRKksrgjCzbryAK7GagDVgO\nzOi0z6vAR+nl14CqPGolSWWQLexHAjsynu9Mr+vObGBVgbWSpBI5M8v29jyOdQ1wKzC5gFpJUgll\nC/tdwKiM56OIeuidfRl4lGjM/mA+tZdeemn7li1bcm2vJCmyBagu1sHOTB8wCQyi65OsFxGNzU8s\noBagXcXzwAMP9HYTBhTfz+LxvSwu8hw9ydaz/wSYA7xIdHXNUmATcHt6+xLgfiAOPJJe10Z0cra7\nWklSmWULe4AX0o9MSzKW/zn9yLVWklRm2a7GUT+TSqV6uwkDiu9n8fhe9q5YbzeAaMy+t9sgSf1K\nLBaDPDI8l2EcSQLg/PPP5+DBg9l3VNHE43EOHDjQ4+PYs5eUs1gshr+v5dXde55vz94xe0kKgGEv\nSQEw7CUpAIa9pAEhmUzy97///ZT1L7/8MmPGjCl7e/J53ccff5yrr766pO3xahxJPVJTs4iWltaS\nHT+RGExdXfa5j2Kx2ImTlie5+uqr2bx5cymadlq99brdMewl9UhLSyvJZG3Jjt/cXLpjh8RhHEkD\nxuuvv864ceM4//zzufXWWzl27Bj19fWMGvXZDXiTySSLFy/mK1/5CsOGDePGG2/k2LFjHdsfffRR\nRo8ezfDhw5kxYwZ79uzp2HbGGWfwyCOPMHr0aCorK7n//vvZsmULkyZN6jhWW1sbwCmvW1dXR3V1\nNZWVlYwbN44VK1aU4R35jGEvaUBob2/nqaeeYvXq1WzZsoV3332XBQsWnDK0E4vFeOaZZ3jxxRfZ\nunUrb731Fo8//jgAa9eu5Z577uGZZ55hz549XHzxxdx4440n1a9evZr169fT0NDAokWLuO2223j6\n6afZvn07Gzdu5Omnn+6yfdXV1bzyyiscPnyYBx54gO9///t88MEHJXkvumLYSxoQYrEYc+bMYeTI\nkcTjce69995ug/fOO+8kkUgQj8e57rrraGxsBGDZsmXMnj2b8ePHM2jQIBYuXMirr77K9u3bO2rv\nvvtuhgwZwtixY/nSl77EtGnTSCaTVFZWMm3aNNavX9/la373u98lkUgAcP311zN69Ghee+21Ir8L\n3TPsJQ0YmcMmF110Ebt37+5yvxOhCzB48GCOHj0K0NGbP+Hcc89l+PDh7Nq1q2PdhRdeeFJt5vOz\nzz6bI0eOdPmaTzzxBBMmTCAejxOPx3n77bfZv39/nv/CwnmCVtKAkdkD3759OyNGjMirfsSIETQ3\nN3c8P3r0KPv372fkyNymz+7qaiCAbdu28aMf/Yi1a9cyadIkYrEYEyZMKOutJ+zZSxoQ2tvb+e1v\nf8uuXbs4cOAAv/zlL08Zbz9dLcBNN93EY489xoYNGzh27Bj33HMPEydO5KKLLspa23k509GjR4nF\nYlxwwQV8+umnPPbYY7z99tt5/Ot6zp69pB5JJAaX9PLIRGJwTvvFYjFmzZrFlClT2L17NzNnzuS+\n++6joaGh2x73iboT27/xjW/wi1/8gu985zscPHiQyZMns3z58pP27aq+q2Nlbhs7dix33XUXkyZN\n4owzzuDmm2/mqquu6rauFLzrpaScedfL8ivWXS/t2fdDhX5jMddvIkoaeAz7fqjQbyz6TUQpXIZ9\nmdkrl9QbDPsys1cuqTd46aUkBcCefZm9/+YaDjU251134HgTUFu0Y0gKi2FfZoNaj/DTqmTedQt2\nNhb1GJLC4jCOJAXAsJcUtKFDh550P5yBymEcST2yqKaG1paWkh1/cCLBvLq6kh3/448/Ltmx+xLD\nXlKPtLa0UJtMluz4tQH0usvBYRxJA0IymaSuru6UaQkh+1SD77//PgCrVq1i3LhxVFZWUlVVxeLF\niwHYt28f06dPJx6PM3z4cL761a923K9m06ZNpFIp4vE4X/ziF3nuuec6jn3LLbdwxx13MH36dCor\nK5k4cWLHa5WbYS9pwOhqWsJcpho8Yfbs2fz+97/n8OHDvPPOO3z9618HYPHixYwaNYp9+/bx4Ycf\nsnDhQmKxGG1tbVx33XVMnTqVvXv38pvf/IZZs2bx7rvvdhzzz3/+M7W1tRw8eJDq6mruvffesrwX\nnRn2kgaE7qYlfOqpp7JONXjCoEGDeOeddzh8+DDnnXceEyZM6Fi/Z88empubqaioYPLkyQA0NDRw\n9OhRampqOPPMM7nmmmuYPn36SdMhfvvb3+byyy+noqKCWbNmdUyBWG6GvaQBo6tpCXfv3n3S5CNd\nTTV4wrPPPsuqVatIJpOkUikaGhoA+NnPfkZ1dTVTpkzh0ksvZdGiRQDs3r37pNcEuPjiizumQ4zF\nYqdMY9jdtIWlZthLGjC6mpZwxIgRbNu2rWP96aYavPzyy1mxYgV79+5l5syZXH/99QAMGTKEhx56\niC1btrBy5Up+9atfsXbtWkaOHMmOHTtOut/8tm3bcp7GsJwMe0kDQnt7O7/73e9OmZYw16kG29ra\nWLZsGR999BEVFRUMHTqUiooKAJ5//nmamppob2+nsrKSiooKKioquPLKKznnnHN48MEHaWtro76+\nnueff77jnEBfmujFSy8l9cjgRKKkl0cOTiRy2i8Wi/G9733vlGkJzz777JynGvzTn/7E3LlzOX78\nOGPGjGHZsmUANDU1MXfuXPbu3Us8HueOO+7ga1/7GgDPPfccP/7xj1m4cCFVVVU8+eSTfOELX+g4\ndufpBks9/WB3nJawzK6tHs99VTPzrluwcwVrmhqLdgypEH15WsJLLrmEpUuXdlxBM1AUa1pCh3Ek\nKQCGvSQFwDF7SQPC1q1be7sJfZo9e0kKgGEvSQEw7CUpAI7ZS8pZPB7vtevEQxWPx4tyHMNeUs4O\nHDjQ201QgRzGkaQAGPaSFIBcwn4qsBl4D5jXxfYxwKvA/wJ3ddrWDLwFrAdeL7iVkqQeyTZmXwE8\nDFwL7ALeAFYCmzL22Q/MBbq6WUs7kAIc6JOkXpStZ38F0ETUQ28DlgMzOu2zF1iX3t4VT91LUi/L\nFvYjgR0Zz3em1+WqHVhD9J/Bbfk1TZJULNmGcXp6L9PJwB7gc8BLRGP/L3feqba2tmM5lUqRSqV6\n+LLKpqZmES0trXnVJBKDqavr6rSNpFKrr6+nvr6+4PpsYb8LyJxgcRRR7z5Xe9I/9wJ/JRoWOm3Y\nqzxaWlpJJmvzqmluzm9/ScXTuSM8f/78vOqzDeOsA0YDSWAQcAPRCdqudB6bPwcYml4+F5gCbMyr\ndZKkosjWs/8EmAO8SHRlzlKiK3FuT29fAiSIrtKpBD4FfgKMBf4B+EvG6ywDVhex7ZKkHOVyu4QX\n0o9MSzKWWzh5qOeEI8D4AtslSSoi740TqPffXMOhxua8ag4cbwJqS9EcSSVm2AdqUOsRflqVzKtm\nwU4nK5f6K++NI0kBMOwlKQCGvSQFwLCXpAB4gjZPi2pqaG1pyatmcCLBvLq6ErVIkrIz7PP0yt9e\nYnbF0Ow7Zlh6fKNhL6lXGfZ5am09zrCqVH41O1eUpjGSlCPH7CUpAIa9JAXAsJekABj2khQAw16S\nAmDYS1IADHtJCoBhL0kBMOwlKQCGvSQFwLCXpAAY9pIUAMNekgJg2EtSAAx7SQqAYS9JATDsJSkA\nhr0kBcCwl6QAGPaSFADDXpICYNhLUgAMe0kKgGEvSQEw7CUpAIa9JAXAsJekABj2khQAw16SAmDY\nS1IADHtJCoBhL0kBMOwlKQCGvSQFwLCXpACc2dsNUP9VU7OIlpbWvGoSicHU1c0rUYskdcewV8Fa\nWlpJJmvzqmluzm9/ScVh2Ktg77+5hkONzXnVHDjeBNSWojmSTiOXsJ8K/BqoAP4ALOq0fQzwGDAB\nuBdYnEet+rFBrUf4aVUyr5oFOxtL0xhJp5XtBG0F8DBRaI8FbgIu67TPfmAu8FABtZKkMsgW9lcA\nTUAz0AYsB2Z02mcvsC69Pd9aSVIZZAv7kcCOjOc70+ty0ZNaSVIRZRuzb+/BsXOura2t7VhOpVKk\nUqkevKwkDTz19fXU19cXXJ8t7HcBozKejyLqoeci59rMsJcknapzR3j+/Pl51WcbxlkHjAaSwCDg\nBmBlN/vGelArSSqhbD37T4A5wItEV9csBTYBt6e3LwESwBtAJfAp8BOiq2+OdFMrSSqzXK6zfyH9\nyLQkY7mFk4drstVKksrMG6FJUgAMe0kKgGEvSQEw7CUpAIa9JAXAsJekABj2khQAw16SAmDYS1IA\nDHtJCoBhL0kBMOwlKQCGvSQFIJe7Xg4Yi2pqaG1pyatmcCLBvLq6ErVIksojqLBvbWmhNpnMq6a2\nubkkbZGkcnIYR5ICEFTP/s03N7KisTm/muMfl6YxklRGQYV9a+txhlWl8qvZuaI0jZGkMnIYR5IC\nYNhLUgAMe0kKgGEvSQEw7CUpAIa9JAXAsJekABj2khQAw16SAmDYS1IADHtJCoBhL0kBMOwlKQCG\nvSQFwLCXpAAY9pIUgKAmL1HfMm1iirZ9h/KuO+uCYbzQUF/8BkkDmGGvXtO27xD3Vc3Mu26Bs4dJ\neXMYR5ICYNhLUgAMe0kKgGEvSQEw7CUpAIa9JAXAsJekABj2khQAw16SAmDYS1IADHtJCkAuYT8V\n2Ay8B8zrZp9/TW/fAEzIWN8MvAWsB14vuJWSpB7JdiO0CuBh4FpgF/AGsBLYlLHPN4FqYDRwJfAI\nMDG9rR1IAQeK1mJJUt6y9eyvAJqIeuhtwHJgRqd9vgX8Mb38GjAMuDBje6zHrZQk9Ui2sB8J7Mh4\nvjO9Ltd92oE1wDrgtsKbKUnqiWzDOO05Hqe73vtVwG7gc8BLRGP/L3feqba2tmM5lUqRSqVyfFlJ\nCkN9fT319fUF12cL+13AqIzno4h67qfbpyq9DqKgB9gL/JVoWOi0YS9JOlXnjvD8+fPzqs82jLOO\n6MRrEhgE3EB0gjbTSuDm9PJE4BDwAXAOMDS9/lxgCrAxr9ZJkooiW8/+E2AO8CLRlTlLia7EuT29\nfQmwiuiKnCbgKPDD9LYE8JeM11kGrC5WwyVJuctlDtoX0o9MSzo9n9NF3fvA+EIaJUkqLr9BK0kB\nMOwlKQCGvSQFwLCXpAAY9pIUAMNekgJg2EtSAAx7SQqAYS9JATDsJSkAudwuQeqzFtXU0NrSknfd\n4ESCeXV1JWiR1DcZ9urXWltaqE0m866rbW4uelukvsywV7/25psbWdHYnH/d8Y+L3xipD+s3Ye+f\n6+pKa+txhlWl8q/buaL4jZH6sH4T9v65LkmF82ocSQpAv+nZOzYrSYXrN2Hv2KwkFc5hHEkKgGEv\nSQEw7CUpAIa9JAXAsJekABj2khQAw16SAmDYS1IADHtJCoBhL0kBMOwlKQCGvSQFwLCXpAD0m7te\nSqVSyCxozoCm/sawV/Be+dtLzK4YmlfN0uMbDXv1K4a9glfIXAnOk6D+xjF7SQqAYS9JATDsJSkA\nhr0kBcCwl6QAGPaSFADDXpICYNhLUgD8UpVUBN5yQX1dnwj72ltu6XK9vwzqL7zlgvq6PhH24xub\nu1zvL4P6C2+5oL6uT4T9sGGpLtf7yyBJxZHLCdqpwGbgPWBeN/v8a3r7BmBCnrWSpBLL1rOvAB4G\nrgV2AW8AK4FNGft8E6gGRgNXAo8AE3OsVZE1Hmpm/LBkbzdjwCjX+1nICV7oX+e16uvrSaVSvd2M\nYGUL+yuAJqA5/Xw5MIOTA/tbwB/Ty68Bw4AEcEkOtSoyw764yvV+FnKCF/rXeS3DvndlC/uRwI6M\n5zuJeu/Z9hkJjMihVhKFneCFk89rhfDXgQqXLezbczxOrKcNkdQzxfjrYNrEFG37DuVVf9YFw3ih\noT7v11XfMhH4j4znP+fUE63/BtyY8XwzcGGOtRAN9bT78OHDh4+8Hk0U0ZnAFiAJDAIagcs67fNN\nYFV6eSLQkEetJKmPmAb8D9H/Ij9Pr7s9/Tjh4fT2DcA/ZqmVJEmSNND4paviagbeAtYDr/duU/qd\nfwc+ADZmrDsfeAl4F1hNdFmxctPV+1lLdFXe+vRjavmb1S+NAv4TeAd4G7gzvb7ffD4riIZ3ksBZ\nOKZfDFuJPgDK39VE3/7ODKcHgbvTy/MAr0/MXVfv5wPAv/ROc/q1BDA+vTyEaGj8MvrR53MSJ1+t\nU5N+qHBbgeG93Yh+LMnJ4XTiyjKIfuE2l7tB/VySU8P+rt5pyoCygujOBHl9Pntz8pLuvoylwrUD\na4B1wG293JaB4EKioQjSPy88zb7KzVyiCzmW0oeHHfqwJNFfTK+R5+ezN8O+vRdfe6CaTPRBmAbc\nQfSntIrjxLXNKtwjRLdRGQ/sARb3bnP6nSHAs8BPgI87bcv6+ezNsN9FdOLhhFFEvXsVbk/6517g\nr0T3NlLhPiD68xjg88CHvdiWgeBDPgulP+DnMx9nEQX9k0TDOJDn57M3w34d0Z0yk0RfurqB6K6Y\nKsw5wInvyp8LTOHk8VLlbyXwg/TyD/jsl0yF+XzG8j/h5zNXMaJhr/8Gfp2xvl99Pv3SVfFcQnRF\nUyPR5Vm+n/l5GtgN/B/RuaQfEl3ZtIZ+cGlbH9T5/bwVeILo0uANRMHkOZDcXAV8SvS7nXnZqp9P\nSZIkSZIkSZIkSZIkSZIkSZIkSerO/wMcyA6FIVzRHwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x68e1e50>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\u984c\n",
      "1\u6642\u9593\u3042\u305f\u308a\u306e\u6765\u5ba2\u6570\u304c\u5e73\u5747 10 \u4eba\u3067\u3042\u308b\u5546\u5e97\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u6765\u5ba2\u6570\u304c\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306b\u5f93\u3046\u3068\u4eee\u5b9a\u3057\u305f\u5834\u5408\u306b\u3001\u3042\u308b1\u6642\u9593\u306b\u3053\u306e\u5546\u5e97\u306b20\u4eba\u4ee5\u4e0a\u306e\u6765\u5ba2\u304c\u3042\u308b\u78ba\u7387\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rv = stats.poisson(10)\n",
      "print u'P(X>=20) = 1-P(X<19) =',1-rv.cdf(19)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X>=20) = 1-P(X<19) = 0.00345434197586\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u5e7e\u4f55\u5206\u5e03\n",
      "\u78ba\u7387 $p$ \u3067\u6210\u529f\u3059\u308b\u72ec\u7acb\u306a\u8a66\u884c(\u30d9\u30eb\u30cc\u30fc\u30a4\u8a66\u884c)\u3092\u7e70\u308a\u8fd4\u3057\u305f\u6642\u306b\u3001\u521d\u3081\u3066\u6210\u529f\u3059\u308b\u307e\u3067\u306e\u8a66\u884c\u56de\u6570 $X=1,2,3,\\ldots$ \u306e\u78ba\u7387\u5206\u5e03\u3092**\u5e7e\u4f55\u5206\u5e03(geometric distribution)**\u3068\u547c\u3073 $\\mathrm{Geom}(X|p)$ \u3068\u66f8\u304d\u307e\u3059\u3002\n",
      "\n",
      "$$ \\mathrm{Geom}(X=k|p) = p(1-p)^{k-1},\\qquad\\mathrm{E}[X]=\\frac{1}{p},\\qquad\\mathrm{V}[X]=\\frac{1-p}{p^2}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Geom(X, 0.1)\n",
      "rv = stats.geom(0.1)\n",
      "x = arange(1, 20)\n",
      "bar(x, rv.pmf(x), align='center')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<Container object of 19 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkiRJkiRJkiRJkiRJkiQ18v9HuTg1u5kpOgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x68d6690>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u4f8b\u984c\n",
      "\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u30663\u56de\u4ee5\u5185\u306b1\u304c\u51fa\u308b\u78ba\u7387\u306f\uff1f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rv = stats.geom(1.0/6)\n",
      "print u'P(X <= 3) =',rv.cdf(3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X <= 3) = 0.421296296296\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u8ca0\u306e\u4e8c\u9805\u5206\u5e03\n",
      "\u78ba\u7387 $p$ \u3067\u6210\u529f\u3059\u308b\u8a66\u884c\u304c $r$ \u56de\u6210\u529f\u3059\u308b\u307e\u3067\u306b\u5fc5\u8981\u306a\u8a66\u884c\u56de\u6570 $X=r,r+1,\\ldots$ \u306e\u5206\u5e03\u3092**\u8ca0\u306e\u4e8c\u9805\u5206\u5e03(negative binomial distribution)**\u3068\u547c\u3073 $\\mathrm{NegBin}(X|r,p)$ \u3068\u66f8\u304d\u307e\u3059\u3002$r=1$ \u306e\u6642\u3053\u308c\u306f\u5e7e\u4f55\u5206\u5e03\u3068\u306a\u308a\u307e\u3059\u306e\u3067\u3001\u5e7e\u4f55\u5206\u5e03\u3092\u4e00\u822c\u5316\u3057\u305f\u5206\u5e03\u3067\u3059\u3002\n",
      "\n",
      "$$\\mathrm{NegBin}(X=k|r,p) = \\binom{k-1}{r-1}p^r(1-p)^{k-r},\\qquad\\mathrm{E}[X] = \\frac{r}{p},\\qquad\\mathrm{V}[X]=\\frac{r(1-p)}{p^2}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\u984c\n",
      "\u30b3\u30a4\u30f3\u3092\u6295\u3052\u30665\u56de\u4ee5\u5185\u306b3\u56de\u8868\u304c\u51fa\u308b\u78ba\u7387\u306f\uff1f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rv = stats.nbinom(3, 0.5)\n",
      "print u'P(X <= 5) =',rv.cdf(5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X <= 5) = 0.85546875\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u8d85\u5e7e\u4f55\u5206\u5e03\n",
      "$K$ \u672c\u5f53\u305f\u308a\u306e\u5165\u3063\u3066\u3044\u308b $N$ \u672c\u306e\u30af\u30b8\u304b\u3089 $n$ \u672c\u53d6\u308a\u51fa\u3057\u305f\u6642\u306b\u3001\u5f53\u305f\u308a\u304c $X=0,1,\\ldots$ \u672c\u3067\u3042\u308b\u78ba\u7387\u306e\u5206\u5e03\u3092**\u8d85\u5e7e\u4f55\u5206\u5e03(hyper geometric distribution)**\u3068\u547c\u3073 $\\mathrm{HyperGeom}(X|N,K,n)$ \u3068\u66f8\u304d\u307e\u3059\u3002\n",
      "\n",
      "$$\\mathrm{HyperGeom}(X=k|N,K,n) = \\frac{\\displaystyle \\binom{n}{k}\\binom{N-n}{K-k}}{\\displaystyle \\binom{N}{K}},\\qquad\\mathrm{E}[X] = \\frac{nK}{N},\\qquad\\mathrm{V}[X] = \\frac{(N-n)n(N-K)K}{(N-1)N^2}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# HyperGeom(X | 1000, 100, 5)\n",
      "rv = stats.hypergeom(1000, 100, 5)\n",
      "x = arange(0, 5+1)\n",
      "bar(x, rv.pmf(x), align='center')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "<Container object of 6 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x6580d10>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$N$ \u304c\u975e\u5e38\u306b\u5927\u304d\u3044\u306a\u3089\u3070\u3001\u30af\u30b8\u3092\u5f15\u304f\u3053\u3068\u306b\u3088\u308b\u672c\u6570\u306e\u5909\u5316\u306f\u7121\u8996\u3067\u304d\u3001\u78ba\u7387 $K/N$ \u3067\u5f53\u305f\u308b\u72ec\u7acb\u306a\u8a66\u884c\u3068\u898b\u306a\u3059\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\u3064\u307e\u308a $N$ \u304c\u5341\u5206\u5927\u304d\u3044\u306a\u3089\u3070\n",
      "\n",
      "$$ \\mathrm{HyperGeom}(X=k|N,K,n) \\approx \\mathrm{Bin}(X=k|n,K/N) $$\n",
      "\n",
      "\u3068\u8fd1\u4f3c\u51fa\u6765\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 1000\n",
      "K = 300\n",
      "n = 100\n",
      "hgeom = stats.hypergeom(N, K, n)\n",
      "binom = stats.binom(n, float(K)/N)\n",
      "x = arange(0, n+1)\n",
      "xlim(0, n)\n",
      "bar(x, hgeom.pmf(x), align='center', alpha=0.3, color='blue', label='hyper geometric')\n",
      "bar(x, binom.pmf(x), align='center', alpha=0.3, color='red', label='binomial')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "<Container object of 101 artists>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Pp3NqXikNj5VubyFp6mrp8a8A7gcWAF8F/mWCbR4APgz8AvhL4Lkp7BuN8rtOaup8Nq80\nc9V6/AuA9YQAvw64Hbi2bJuVwDXAUuBO4MEp7BuV7duepHV3kdbdRbZve/Ki9f0HX8igqsZUqS1K\nF7oNj5xl68aN9PX20tfby9aNG+e4wrlTKBSyLqFh2Bb1US34u4ADwEFgFHgUWF22za3Aw8nrHcAi\n4Moa92166XB6Ze/Lk96D5tn/M/hLammLah+kzcKwO8+2qI9qQz3twOHU/BHgxhq2aQeuqmHfprd9\n25PcuHARACdfO55xNc2ldHAcYPtjPXzmzz4BwKVXXkb3v/5TlqVJDa1a8Nd605iWmRYyn3V/+h8Y\nPnYSCKEDMHzsJJdeedkF4TQ29t3Mamx2b3vzDH/a+WEAHhvYcu5nkv55AJz8+Wv80S3LAW8BIVWy\nDPheav4eYF3ZNr3AR1Lz+4AratwXwnDQuJOTk5PTlKYDzJJWYADoANqA55n44O4TyetlwI+nsK8k\nqQF9GHiZ8OlyT7LsrmQqWZ+s3wXcUGVfSZIkSbFYQTgmsJ+Jx/+b2RLgh8Ae4EXgk8nyy4H/Bn4C\nbCOcHhuDBYQL//qS+VjbAcL3ugnYC7xEOBsuxva4h/D78QLwDeAS4mmH/wCOE773ksm+93sIOboP\nuHmOapyWBYQhoA5gIfEdA7gS+O3k9aWEIbFrgS8An0uWrwP+ee5Ly8SngUeAzcl8rO0A4bqYv0pe\ntwLvJr726ABeIYQ9wLeAjxNPO3wAuJ4Lg7/S934dIT8XEtrtAA18O57f48Kzfj6fTLF6HLiJ82dF\nQfhw2JdZRXNnMfB94EOc7/HH2A4QQv6VCZbH1h6XEzpDlxE+/PqAPySudujgwuCv9L2XnzH5PcKJ\nNhVl+alQ6cKvGHUQPt13EH6wpSu9jnP+B93MvgR8FngrtSzGdgC4GngD+BrwLPAV4J3E1x4ngC8C\nh4CjwBBhmCO2dkir9L1fRcjPkqpZmmXwj2f4tRvJpcC3gbuBU2XrSufrNrNbgNcJ4/uVLgSMoR1K\nWglnxn05+XeEi/8SjqE9OoFPETpFVxF+Tz5atk0M7VBJte990nbJMviLhAOcJUu48FMrBgsJof+f\nhKEeCJ/kVyavf40Qis3sfYT7Pb0KfBP4A0J7xNYOJUeS6ZlkfhPhA+AYcbXHe4EfAYPAGPAdwvBw\nbO2QVul3ojxLFyfLKsoy+HcS7ujZQbjA6zbOH9iLQQvwEOGsjftTyzcTDmKR/Ps4ze1ewn/aqwlX\ngP8A+Avia4eSY4Qh0Pck8zcRzmzpI6722EcYp3474XflJsLvSmztkFbpd2Iz4XenjfB7tBR4es6r\nm4KYL/B6P2FM+3nCMMdzhNNbLycc6Gz209Um8kHOf/jH3A6/Rejx7yL0dN9NnO3xOc6fzvkw4S/k\nWNrhm4RjG2cIHYE7mPx7v5eQo/uA5XNaqSRJkiRJkiRJkiRJkiRJkiRJkiTpvP8H7n9FRjxSgTAA\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7145f90>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# \u9023\u7d9a\u5206\u5e03"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u4e00\u69d8\u5206\u5e03\n",
      "\u533a\u9593 $[a,b]$ \u306b\u304a\u3051\u308b\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u304c\n",
      "\n",
      "$$\\pi(x) = \\frac{1}{b-a}$$\n",
      "\n",
      "\u3067\u305d\u308c\u4ee5\u5916\u306f $0$ \u3067\u3042\u308b\u5206\u5e03\u3092**\u9023\u7d9a\u4e00\u69d8\u5206\u5e03(continuous uniform distribution)**\u3068\u547c\u3073$\\mathrm{U}(X|a,b)$\u3068\u66f8\u304d\u307e\u3059\u3002\u7279\u306b $\\mathrm{U}(X)\\stackrel{\\mathrm{def}}{=}\\mathrm{U}(X|0,1)$ \u3092\u6a19\u6e96\u4e00\u69d8\u5206\u5e03\u3068\u8a00\u3044\u307e\u3059\u3002\u3053\u308c\u306f $[a,b]$ \u5185\u306e\u5b9f\u6570\u3092\u5168\u304f\u7121\u4f5c\u70ba\u306b\u9078\u3076\u3068\u3044\u3046\u8a66\u884c\u306e\u78ba\u7387\u5206\u5e03\u3067\u3059\u3002\n",
      "\n",
      "$$\\mathrm{E}[X] = \\frac{a+b}{2},\\qquad\\mathrm{V}[X] = \\frac{(b-a)^2}{12}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# pdf(x)\u304c\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\n",
      "a = 1.0\n",
      "b = 2.0\n",
      "x = linspace(0, 3)\n",
      "ylim(0,1.1)\n",
      "plot(x, stats.uniform(a, b-a).pdf(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "[<matplotlib.lines.Line2D at 0x73a5650>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD7CAYAAACRxdTpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmS8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x73a3110>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u9023\u7d9a\u4e00\u69d8\u5206\u5e03\u306b\u95a2\u3057\u3066\u91cd\u8981\u306a\u70b9\u306f\u3001\u4efb\u610f\u306e\u9023\u7d9a\u7684\u306a\u78ba\u7387\u5206\u5e03\u306b\u5bfe\u3057\u3066**\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306e\u5024\u306f\u6a19\u6e96\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046**\u3068\u3044\u3046\u4e8b\u5b9f\u3067\u3059\u3002\n",
      "\u3064\u307e\u308a\u3001\u9023\u7d9a\u78ba\u7387\u5909\u6570 $X$ \u306b\u5bfe\u3057\u3066 $y=F(x)=P(X\\leq x)$ \u3068\u7f6e\u304f\u3068 $Y\\sim U$ \u3068\u306a\u308b\u3068\u3044\u3046\u4e8b\u3067\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u8a3c\u660e\u3011\n",
      "\n",
      "$X$ \u306e\u5f93\u3046\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092 $\\pi_X(x),F_X(x)$ \u3068\u3059\u308b\u3002$y=F_X(x)$ \u3068\u7f6e\u63db\u3059\u308b\u3068$ 0\\leq y\\leq 1$ \u3067\u3042\u308a\n",
      "$$ \\pi_Y(y) = \\frac{1}{|F_X'(F_X^{-1}(y))|}\\pi_X(F_X^{-1}(y)) = \\frac{1}{\\pi_X(F_X^{-1}(y))}\\pi_X(F_X^{-1}(y)) = 1$$\n",
      "\u3068\u306a\u308b\u306e\u3067 $Y\\sim U$ \u3067\u3042\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "\u5f93\u3063\u3066\u3001\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u306e\u9006\u95a2\u6570\u3092\u5229\u7528\u3059\u308c\u3070\u6a19\u6e96\u4e00\u69d8\u5206\u5e03\u306b\u5f93\u3046\u4e71\u6570\u304b\u3089\u4efb\u610f\u306e\u5206\u5e03\u306b\u5f93\u3046\u4e71\u6570\u3092\u751f\u6210\u3059\u308b\u4e8b\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u8a73\u3057\u304f\u306f\u6b21\u56de\u8aac\u660e\u3057\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u6b63\u898f\u5206\u5e03\n",
      "\u5b9a\u6570 $\\mu$ \u3068$\\sigma>0$ \u306b\u5bfe\u3057\u3066\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u304c\n",
      "\n",
      "$$ \\pi(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left\\{-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right\\} $$\n",
      "\n",
      "\u3068\u8868\u3055\u308c\u308b\u5206\u5e03\u3092**\u6b63\u898f\u5206\u5e03(normal distribution)**\u3068\u547c\u3073\uff0c$\\mathrm{N}(X|\\mu,\\sigma^2)$ \u3068\u66f8\u304d\u307e\u3059\u3002\u7279\u306b $\\mathrm{N}(X|0,1)$ \u3092\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u3068\u547c\u3073\u307e\u3059\u3002\u6570\u5b66\u8005\u30ab\u30fc\u30eb\u30fb\u30d5\u30ea\u30fc\u30c9\u30ea\u30d2\u30fb\u30ac\u30a6\u30b9\u306e\u540d\u3092\u53d6\u3063\u3066**\u30ac\u30a6\u30b9\u5206\u5e03(Gaussian distribution)**\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002\n",
      "\n",
      "$$\\mathrm{E}[X] = \\mu,\\qquad\\mathrm{V}[X] = \\sigma^2$$\n",
      "\n",
      "\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5e73\u5747 $x=\\mu$ \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u5bfe\u79f0\u7684\u306a\u91e3\u9418\u578b\u306e\u5206\u5e03\u3067\u3059\u3002\u9023\u7d9a\u578b\u5206\u5e03\u306e\u4e2d\u3067\u6700\u3082\u91cd\u8981\u306a\u5206\u5e03\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rv = stats.norm(0, 1)\n",
      "x = linspace(-4, 4)\n",
      "plot(x, rv.pdf(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "[<matplotlib.lines.Line2D at 0x7c1ad90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7jiaYNBdNhnr3Xbj9dpg8WcldgunQQ20R+KlTbQilpIbGXATMunVWd3/uOTjp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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6e24150>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u5909\u6570 $X$ \u304c\u5e73\u5747\u304b\u3089 $\\pm\\sigma$ \u4ee5\u5185\u3001$\\pm2\\sigma$ \u4ee5\u5185\uff0c$\\pm 3\\sigma$ \u4ee5\u5185\u306b\u5165\u308b\u78ba\u7387\u306f\u662f\u975e\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rv = stats.norm(0, 1)\n",
      "print u'1\u03c3\u4ee5\u5185:', rv.cdf(1)-rv.cdf(-1)\n",
      "print u'2\u03c3\u4ee5\u5185:', rv.cdf(2)-rv.cdf(-2)\n",
      "print u'3\u03c3\u4ee5\u5185:', rv.cdf(3)-rv.cdf(-3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\u03c3\u4ee5\u5185: 0.682689492137\n",
        "2\u03c3\u4ee5\u5185: 0.954499736104\n",
        "3\u03c3\u4ee5\u5185: 0.997300203937\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rv = stats.norm(0, 1)\n",
      "x = linspace(-4, 4)\n",
      "x1 = x[logical_and(-1 <= x, x <= 1)] # 1\u03c3\u4ee5\u5185\n",
      "x2 = x[logical_and(-2 <= x, x <= 2)] # 2\u03c3\u4ee5\u5185\n",
      "x3 = x[logical_and(-3 <= x, x <= 3)] # 3\u03c3\u4ee5\u5185\n",
      "fill_between(x3, 0, rv.pdf(x3), alpha=0.3, color='red', label=u'3\u03c3\u4ee5\u5185')\n",
      "fill_between(x2, 0, rv.pdf(x2), alpha=0.3, color='purple', label=u'2\u03c3\u4ee5\u5185')\n",
      "fill_between(x1, 0, rv.pdf(x1), alpha=0.3, color='blue', label=u'1\u03c3\u4ee5\u5185')\n",
      "plot(x, rv.pdf(x), color='black')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "[<matplotlib.lines.Line2D at 0x8081990>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/T4BKpq9uGPcnJirMUpT/ADOARUUtpKVTtb4E/k91CAvMj/vyAbRz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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7bee1d0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4f8b\u3048\u3070\u3001\u5b66\u6821\u3067\u306e\u8a66\u9a13\u306b\u304a\u3051\u308b\u504f\u5dee\u5024\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u504f\u5dee\u5024\u3068\u306f\u5f97\u70b9\u5206\u5e03\u3092\u5e73\u5747\u304c $50$, \u6a19\u6e96\u504f\u5dee\u304c $10$ \u306b\u306a\u308b\u3088\u3046\u306b\u8abf\u6574\u3057\u305f\u3082\u306e\u3067\u3059\u3002\u5f97\u70b9\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u5834\u5408\u306b\u306f\u4e0a\u306e\u6570\u5024\u3092\u4f7f\u3046\u3053\u3068\u304c\u51fa\u6765\u3066\u3001\n",
      "\n",
      "* \u504f\u5dee\u5024\u304c 40\uff5e60 \u306e\u4eba\u304c\u5168\u4f53\u306e68.3%\n",
      "* \u504f\u5dee\u5024\u304c 30\uff5e70 \u306e\u4eba\u304c\u5168\u4f53\u306e95.4%\n",
      "* \u504f\u5dee\u5024\u304c 20\uff5e80 \u306e\u4eba\u304c\u5168\u4f53\u306e99.7%\n",
      "\n",
      "\u3068\u5224\u308a\u307e\u3059\u3002\u5206\u5e03\u306e\u5bfe\u79f0\u6027\u3092\u8003\u3048\u308c\u3070\u3001\u4f8b\u3048\u3070\u504f\u5dee\u5024\u304c70\u4ee5\u4e0a\u306e\u4eba\u306f\u5168\u4f53\u306e $(100 - 95.4)/2 = 2.3$% \u3067\u3042\u308b\u3068\u3044\u3063\u305f\u8a08\u7b97\u304c\u51fa\u6765\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\n",
      "\n",
      "\u6b63\u898f\u5206\u5e03\u304c\u91cd\u8981\u3067\u3042\u308b\u7406\u7531\u306e\uff11\u3064\u306b**\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406(central limit theorem)**\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u3011\n",
      "\n",
      "$X_1,X_2,\\ldots,X_n$ \u304ci.i.d.\u3067\u305d\u306e\u5e73\u5747\u304c $\\mu$, \u5206\u6563 $\\sigma^2$ \u306e\u3068\u304d\u3001\u305d\u306e\u5e73\u5747\u5024(\u6a19\u672c\u5e73\u5747)\n",
      "\n",
      "$$\\overline{\\mathbf{X}} = \\frac{X_1 + X_2 + \\cdots + X_n}{n}$$\n",
      "\n",
      "\u306e\u5f93\u3046\u5206\u5e03\u306f $n$ \u304c\u5341\u5206\u5927\u304d\u3044\u6642 $\\mathrm{N}\\left(\\mu,\\frac{\\sigma^2}{n}\\right)$ \u3067\u8fd1\u4f3c\u51fa\u6765\u308b\u3002\n",
      "(\u53b3\u5bc6\u306b\u306f\u5206\u5e03\u53ce\u675f\u3068\u3044\u3046\u6982\u5ff5\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u3053\u3053\u3067\u306f\u7701\u7565\u3057\u307e\u3059\u3002)\n",
      "\n",
      "----\n",
      "\n",
      "\u5206\u6563\u304c\u5b58\u5728\u3059\u308b\u5206\u5e03(\u73fe\u5b9f\u306b\u767b\u5834\u3059\u308b\u6b86\u3069\u306e\u5206\u5e03)\u306b\u3064\u3044\u3066\u3053\u308c\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u4f8b\u3068\u3057\u3066\u30b5\u30a4\u30b3\u30ed\u3067\u5b9f\u9a13\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u307e\u305a\u3001\u30b5\u30a4\u30b3\u30ed\u3092 $N$ \u56de\u632f\u3063\u3066\u5e73\u5747\u5024\u3092\u51fa\u3059\u70ba\u306b\u306f\u6b21\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002\u4f55\u3089\u304b\u306e\u6570\u5024\u304c\u51fa\u305f\u3068\u601d\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dice = stats.randint(1, 6+1) # \u30b5\u30a4\u30b3\u30ed\u3092\u7528\u610f\n",
      "N = 100\n",
      "dice.rvs(N).mean() # \u30b5\u30a4\u30b3\u30ed\u3092 N \u56de\u632f\u3063\u3066\u5e73\u5747\u3092\u6c42\u3081\u308b\u3002"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "4.0300000000000002"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u3053\u308c\u3092 $M$ \u56de\u884c\u3063\u3066\u3001\u305d\u306e\u7d50\u679c\u306e\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u63cf\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = 10000\n",
      "result = dice.rvs((M, N)).mean(axis=1) # MxN\u56de\u30b5\u30a4\u30b3\u30ed\u3092\u632f\u3063\u3066\u3001N\u306b\u3064\u3044\u3066(axis=1)\u5e73\u5747\u3092\u53d6\u308b\u3002\n",
      "hist(result, bins=20, normed=True) # \u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u4f5c\u6210"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "(array([ 0.00701754,  0.03859649,  0.08245614,  0.1754386 ,  0.44035088,\n",
        "         0.7       ,  0.99824561,  1.60701754,  2.0122807 ,  1.9877193 ,\n",
        "         2.46842105,  2.23684211,  1.77017544,  1.10526316,  0.92105263,\n",
        "         0.53157895,  0.23859649,  0.15614035,  0.05263158,  0.01403509]),\n",
        " array([ 2.92 ,  2.977,  3.034,  3.091,  3.148,  3.205,  3.262,  3.319,\n",
        "         3.376,  3.433,  3.49 ,  3.547,  3.604,  3.661,  3.718,  3.775,\n",
        "         3.832,  3.889,  3.946,  4.003,  4.06 ]),\n",
        " <a list of 20 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlG66AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x73baad0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u30b5\u30a4\u30b3\u30ed\u306e\u51fa\u76ee\u306e\u5e73\u5747\u306f $3.5$, \u5206\u6563\u306f$2.92$ \u306a\u306e\u3067\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u306b\u3088\u308c\u3070\u3001\u3053\u308c\u304c $\\mathrm{N}(3.5,2.92/N)$ \u3067\u8fd1\u4f3c\u51fa\u6765\u308b\u306f\u305a\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu  = dice.mean() # \u30b5\u30a4\u30b3\u30ed\u306e\u5e73\u5747\n",
      "var = dice.var()  # \u30b5\u30a4\u30b3\u30ed\u306e\u5206\u6563\n",
      "\n",
      "hist(result, bins=20, normed=True) # \u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\n",
      "\n",
      "x = linspace(3.0, 4.0)\n",
      "plot(x, stats.norm(mu, sqrt(var/N)).pdf(x), color='red') # \u6b63\u898f\u5206\u5e03N(\u03bc, \u03c3^2/N) \u3092\u63cf\u304f"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "[<matplotlib.lines.Line2D at 0x82f3b90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7wSefWNMIvP02fPopwwFN2ysC31CPK1nIIq5gJc14nEFU4oDpWK6m4p4IGzZA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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x82f3bd0>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u6a19\u6e96\u5316\n",
      "\n",
      "\u6b63\u898f\u5206\u5e03\u3067\u306f $X\\sim\\mathrm{N}(\\mu,\\sigma^2)$ \u306a\u3089\u3070\uff0c $a+bX \\sim \\mathrm{N}(a+b\\mu, b^2\\sigma^2)$ \u3068\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "\u305d\u3053\u3067 $X\\sim\\mathrm{N}(\\mu,\\sigma^2)$ \u3067\u3042\u308b\u5909\u6570\u306b\u5bfe\u3057\u3066\n",
      "\n",
      "$$ Z = \\frac{X-\\mu}{\\sigma} $$\n",
      "\n",
      "\u3068\u7f6e\u304d\u76f4\u3059\u3068$ Z \\sim \\mathrm{N}(0, 1)$ \u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u64cd\u4f5c\u3092\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306e**\u6a19\u6e96\u5316(normalization)**\u3068\u547c\u3073\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u518d\u751f\u6027\n",
      "\n",
      "\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u306f**\u518d\u751f\u6027(reductive property)**\u3068\u3044\u3046\u3068\u3066\u3082\u826f\u3044\u6027\u8cea\u3092\u6301\u3061\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u6b63\u898f\u5206\u5e03\u306e\u518d\u751f\u6027\u3011\n",
      "\n",
      "$X_1,X_2$ \u304c\u305d\u308c\u305e\u308c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u306a\u3089\u3070\u3001$X_1+X_2$ \u3082\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3002\n",
      "\n",
      "\u5177\u4f53\u7684\u306b\u306f$X_1\\sim \\mathrm{N}(\\mu_1,\\sigma_1^2),X_2\\sim\\mathrm{N}(\\mu_2,\\sigma_2^2)$ \u306a\u3089\u3070 $X_1+X_2\\sim\\mathrm{N}(\\mu_1+\\mu_2, \\sigma_1^2+\\sigma_2^2)$\u3067\u3042\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "\u4f8b\u3048\u3070\u3001\u3042\u308b\u5b66\u6821\u3067\u884c\u3063\u305f\u306e\u8a66\u9a13\u306e\u5f97\u70b9\u5206\u5e03\u304c\n",
      "\n",
      "- \u6570\u5b66\u306e\u70b9\u6570: \u5e73\u5747\u70b9 $53$ \u70b9, \u6a19\u6e96\u504f\u5dee $11$ \u70b9\u306e\u6b63\u898f\u5206\u5e03\n",
      "- \u82f1\u8a9e\u306e\u70b9\u6570: \u5e73\u5747\u70b9 $72$ \u70b9, \u6a19\u6e96\u504f\u5dee $7$ \u70b9\u306e\u6b63\u898f\u5206\u5e03\n",
      "\n",
      "\u3067\u3042\u3063\u305f\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u3059\u308b\u3068\n",
      "\n",
      "- \u6570\u5b66\u306e\u70b9\u6570 + \u82f1\u8a9e\u306e\u70b9\u6570: \u5e73\u5747\u70b9 $125$ \u70b9\u3001\u6a19\u6e96\u504f\u5dee $\\sqrt{11^2 + 7^2} = 13.0$ \u70b9\u306e\u6b63\u898f\u5206\u5e03\n",
      "\n",
      "\u3068\u3044\u3046\u4e8b\u306b\u306a\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u6b63\u898f\u5206\u5e03\u3068\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\n",
      "\n",
      "\u5e73\u5747\u304c $\\mu$, \u5206\u6563\u304c $\\sigma^2$ \u3067\u3042\u308b\u5206\u5e03 $\\pi(x)$ \u3067\u3001\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\n",
      "\n",
      "$$\\mathrm{H}(\\pi) = -\\int_{-\\infty}^\\infty \\pi(x)\\log\\pi(x)\\mathrm{d}x$$\n",
      "\n",
      "\u304c\u6700\u5927\u306b\u306a\u308b\u5206\u5e03\u304c\u5b9f\u306f\u6b63\u898f\u5206\u5e03 $\\mathrm{N}(X|\\mu,\\sigma^2)$ \u3067\u3059\u3002\u3064\u307e\u308a\u3001\u5e73\u5747\u30fb\u5206\u6563\u4ee5\u5916\u306b\u4f59\u8a08\u306a\u69cb\u9020\u3092\u4eee\u5b9a\u3057\u306a\u3044(\u3064\u307e\u308a\u6700\u3082\u4e71\u96d1\u306a)\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u306b\u306a\u308a\u307e\u3059\u3002\u7d71\u8a08\u5b66\u3067\u306f\u672a\u77e5\u306e\u5206\u5e03\u306b\u5bfe\u3057\u3066\u305d\u308c\u304c\u6b63\u898f\u5206\u5e03\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3044\u3046\u4e8b\u3092\u826f\u304f\u884c\u3044\u307e\u3059\u304c\u3001\u305d\u308c\u304c\u59a5\u5f53\u3067\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u308b\u306e\u306f\u3053\u306e\u305f\u3081\u3067\u3059\u3002\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u6700\u5927\u5316\u306b\u3088\u308b\u5206\u5e03\u306e\u5c0e\u51fa\u65b9\u6cd5\u306f\u899a\u3048\u3066\u304a\u304f\u4fa1\u5024\u304c\u3042\u308b\u3068\u601d\u3046\u306e\u3067\u3001\u4ee5\u4e0b\u306b\u8a3c\u660e\u3092\u66f8\u3044\u3066\u304a\u304d\u307e\u3059\u3002\n",
      "\n",
      "---\n",
      "\u3010\u8a3c\u660e\u3011\n",
      "\n",
      "\u5e73\u5747\u5024\u304c $\\mu$, \u5206\u6563\u304c $\\sigma^2$ \u3067\u3042\u308b\u3068\u3044\u3046\u6761\u4ef6\u4e0b\u3067\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u6700\u5927\u306b\u3059\u308b $\\pi(x)$ \u3092\u6c42\u3081\u308b\u3002\u305d\u306e\u70ba\u306b\u306f\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u306e\u672a\u5b9a\u4e57\u6570 $\\alpha,\\beta,\\gamma$ \u3092\u5c0e\u5165\u3057\u3066\n",
      "\n",
      "$$ \\begin{aligned}\n",
      "F(\\pi,\\alpha,\\beta,\\gamma) &= -\\int_{-\\infty}^\\infty\\pi(x)\\log \\pi(x)\\mathrm{d}x-\\alpha\\left(\\int_{-\\infty}^\\infty\\pi(x)\\mathrm{d}x-1\\right)\n",
      "-\\beta\\left(\\int_{-\\infty}^\\infty x\\pi(x)\\mathrm{d}x-\\mu\\right)-\\gamma\\left(\\int_{-\\infty}^\\infty(x-\\mu)^2\\pi(x)\\mathrm{d}x-\\sigma^2\\right)\\\\\n",
      " &= -\\int_{-\\infty}^\\infty\\{\\pi(x)\\log \\pi(x)+\\alpha\\pi(x)+\\beta x\\pi(x) + \\gamma(x-\\mu)^2\\pi(x)\\}\\mathrm{d} x + \\alpha + \\mu\\beta + \\sigma^2\\gamma\n",
      "\\end{aligned}$$\n",
      "\n",
      "\u304c\u505c\u7559\u70b9\u3092\u53d6\u308b\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u826f\u3044\u3002\u3059\u306a\u308f\u3061\u3001\u5404\u5909\u6570\u3067\u5fae\u5206($\\pi$\u306f\u95a2\u6570\u306a\u306e\u3067\u5909\u5206)\u3057\u305f\u4ee5\u4e0b\u304c\u5168\u3066 $0$ \u3068\u306a\u308c\u3070\u826f\u3044\u3002\n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\frac{\\delta F}{\\delta \\pi} &= -\\int_{-\\infty}^\\infty\\{\\log \\pi(x) + 1 + \\alpha + \\beta x + \\gamma(x-\\mu)^2\\}\\mathrm{d}x\\qquad\\cdots(1) \\\\\n",
      "\\frac{\\partial F}{\\partial \\alpha} &= -\\int_{-\\infty}^\\infty\\pi(x)\\mathrm{d}x+1 \\qquad\\cdots(2)\\\\\n",
      "\\frac{\\partial F}{\\partial \\beta} &= -\\int_{-\\infty}^\\infty x\\pi(x)\\mathrm{d}x + \\mu \\qquad\\cdots(3)\\\\\n",
      "\\frac{\\partial F}{\\partial \\gamma} &= -\\int_{-\\infty}^\\infty (x-\\mu)^2\\pi(x)\\mathrm{d}x + \\sigma^2 \\qquad\\cdots(4)\n",
      "\\end{aligned}$$\n",
      "\n",
      "\u307e\u305a(1)\u304c$\\pi$\u306e\u5fae\u5c0f\u5909\u5316\u306b\u5bfe\u3057\u3066 $0$ \u306b\u306a\u308b\u70ba\u306b\u306f\u7a4d\u5206\u306e\u4e2d\u304c $0$ \u3067\u3042\u308b\u4e8b\u304c\u5fc5\u8981\u3060\u304b\u3089\n",
      "\n",
      "$$\\log \\pi(x) + 1 + \\alpha + \\beta x + \\gamma(x-\\mu)^2 = 0$$ \n",
      "\n",
      "\u3064\u307e\u308a\n",
      "\n",
      "$$ \\pi(x) = \\exp\\{-1-\\alpha-\\beta x-\\gamma(x-\\mu)^2\\}\\qquad\\cdots(5)$$\n",
      "\n",
      "\u3068\u8868\u3055\u308c\u308b\u4e8b\u304c\u5fc5\u8981\u3002\u3053\u3053\u3067 \n",
      "$$y = \\sqrt{\\gamma}\\left(x - \\mu + \\frac{\\beta}{2\\gamma}\\right)=\\sqrt{\\gamma}(x-\\delta)\\qquad\\left(\\delta=\\mu-\\frac{\\beta}{2\\gamma}\\right)$$\n",
      "\u3068\u7f6e\u304d\u63db\u3048\u308b\u3068\n",
      "\n",
      "$$ \\pi(x) = \\exp\\left\\{-y^2-1-\\alpha-\\beta\\mu+\\frac{\\beta^2}{4\\gamma}\\right\\}=\\epsilon e^{-y^2}\\qquad\\left(\\epsilon=\\exp\\left\\{-1-\\alpha-\\beta\\mu+\\frac{\\beta^2}{4\\gamma}\\right\\}\\right)$$\n",
      "\n",
      "\u3068\u306a\u308b\u306e\u3067\u3001\n",
      "\n",
      "$$\\int_{-\\infty}^\\infty\\pi(x)\\mathrm{d}x = \\frac{\\epsilon}{\\sqrt{\\gamma}}\\int_{-\\infty}^\\infty e^{-y^2}\\mathrm{d}y = \\epsilon\\sqrt{\\frac{\\pi}{\\gamma}}$$\n",
      "$$\\int_{-\\infty}^\\infty x\\pi(x)\\mathrm{d}x = \\frac{\\epsilon}{\\sqrt{\\gamma}}\\int_{-\\infty}^\\infty\\left(\\frac{y}{\\sqrt{\\gamma}}+\\delta\\right)e^{-y^2}\\mathrm{d}y = \\delta\\epsilon\\sqrt{\\frac{\\pi}{\\gamma}}$$\n",
      "$$\\int_{-\\infty}^\\infty (x-\\mu)^2\\pi(x)\\mathrm{d}x = \\frac{\\epsilon}{\\sqrt{\\gamma}}\\int_{-\\infty}^\\infty\\left(\\frac{y}{\\sqrt{\\gamma}}+\\delta-\\mu\\right)^2e^{-y^2}\\mathrm{d}y = \\frac{\\epsilon}{\\sqrt{\\gamma}}\\left(\\frac{\\sqrt{\\pi}}{2\\gamma}+(\\delta-\\mu)^2\\sqrt{\\pi}\\right)$$\n",
      "\n",
      "\u5f93\u3063\u3066 (2)(3)(4)\u3088\u308a\n",
      "$$\\epsilon\\sqrt{\\frac{\\pi}{\\gamma}} = 1,\\quad \\delta\\epsilon\\sqrt{\\frac{\\pi}{\\gamma}}=\\mu,\\quad \\frac{\\epsilon}{\\sqrt{\\gamma}}\\left(\\frac{\\sqrt{\\pi}}{2\\gamma}+(\\delta-\\mu)^2\\sqrt{\\pi}\\right)=\\sigma^2$$\n",
      "\u3067\u3042\u308b\u3002\u6700\u521d\u306e2\u5f0f\u3088\u308a $\\delta=\\mu$ \u306a\u306e\u3067 $\\beta = 0$\u3002\u307e\u305f\u7b2c\uff11,3\u5f0f\u3088\u308a $1/(2\\gamma)=\\sigma^2$ \u3064\u307e\u308a $\\gamma=1/(2\\sigma^2)$ \u3002\u307e\u305f $\\epsilon=1/\\sqrt{2\\pi\\sigma^2}$\u3002\u3088\u3063\u3066$1/\\sqrt{2\\pi\\sigma^2} = \\exp(1-\\alpha)$ \u4ee5\u4e0a\u3092 (5) \u306b\u4ee3\u5165\u3057\u3066\n",
      "\n",
      "$$\\pi(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left\\{-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right\\} $$\n",
      "\n",
      "----"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4e8c\u9805\u5206\u5e03\u3068\u306e\u95a2\u4fc2\n",
      "\n",
      "$X_1,\\ldots,X_n\\stackrel{\\text{i.i.d.}}{\\sim}\\mathrm{Bern}(p)$ \u306e\u6642\n",
      "$$ X_1  + \\cdots + X_n \\sim \\mathrm{Bin}(n,p)$$\n",
      "\u3067\u3057\u305f\u3002\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u306e\u5e73\u5747\u306f $p$, \u5206\u6563\u306f $p(1-p)$ \u306a\u306e\u3067\u3001\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u3088\u308a $n$ \u304c\u5341\u5206\u5927\u304d\u3044\u3068\u304d $\\overline{X}\\sim\\mathrm{N}(p, p(1-p)/n)$ \u3068\u306a\u308a\u307e\u3059\u3002\u5f93\u3063\u3066 $X_1 + \\cdots + X_n = n\\overline{X}$ \u306a\u306e\u3067 $n$ \u304c\u5341\u5206\u5927\u304d\u3044\u6642\n",
      "$$ X_1 + \\cdots + X_n \\sim \\mathrm{N}(np,np(1-p))$$\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u304b\u3089\u4e8c\u9805\u5206\u5e03\u3092\u6b63\u898f\u5206\u5e03\u3067\u8fd1\u4f3c\u51fa\u6765\u308b(\u9006\u3082\u3057\u304b\u308a)\u4e8b\u304c\u5224\u308a\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "$n$ \u304c\u5341\u5206\u5927\u304d\u3044\u6642\n",
      "\n",
      "$$\\mathrm{Bin}(X|n,p)\\approx\\mathrm{N}(X|np,np(1-p))$$\n",
      "\n",
      "\u3068\u8fd1\u4f3c\u51fa\u6765\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "\u3053\u306e\u95a2\u4fc2\u306f\u5f8c\u306b $p$ \u306e\u533a\u9593\u63a8\u5b9a\u306a\u3069\u3067\u5b9f\u969b\u306b\u4f7f\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 100\n",
      "p = 0.3\n",
      "mu    = n*p\n",
      "sigma = sqrt(n*p*(1-p))\n",
      "xlim(mu-3*sigma, mu + 3*sigma)\n",
      "x = arange(int(mu-3*sigma), int(mu+3*sigma))\n",
      "bar(x, stats.binom(n,p).pmf(x), align='center', width=0.5)\n",
      "plot(x, stats.norm(mu, sigma).pdf(x), color='red')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "[<matplotlib.lines.Line2D at 0x8449810>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9++tCahKosHvB4cPwwANmnfWTTnI6G5Hy0bcv7N0Lr73mdCael2hh74DZy3Qj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\nREREREREREREREREREREREREJHH/H0RjtSKqDRRYAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8449a10>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u591a\u6b21\u5143\u6b63\u898f\u5206\u5e03\n",
      "\n",
      "\u591a\u6b21\u5143\u306e\u6b63\u898f\u5206\u5e03\u3082\u540c\u69d8\u306b\u8003\u3048\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\u5e73\u5747\u304c $\\boldsymbol{\\mu}$, \u5206\u6563\u5171\u5206\u6563\u884c\u5217\u304c $\\boldsymbol{\\Sigma}$ \u3067\u3042\u308b\u69d8\u306a\u5206\u5e03\u3067\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u304c\u6700\u5927\u306e\u7269\u3092\u6c42\u3081\u308b\u3068\u591a\u6b21\u5143\u6b63\u898f\u5206\u5e03\u306e\u5bc6\u5ea6\u95a2\u6570\u306e\u65b9\u7a0b\u5f0f\n",
      "\n",
      "$$ \\mathrm{N}(\\mathbf{x}|\\boldsymbol{\\mu},\\boldsymbol{\\Sigma}) =\\frac{1}{\\sqrt{(2\\pi)^d|\\boldsymbol{\\Sigma}|}}\\exp\\left\\{-\\frac{1}{2}(\\mathbf{x}-\\boldsymbol{\\mu})^T\\boldsymbol{\\Sigma}^{-1}(\\mathbf{x}-\\boldsymbol{\\mu})\\right\\} \\qquad \\text{($d$\u306f\u6b21\u5143)}$$\n",
      "\n",
      "\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u591a\u6b21\u5143\u6b63\u898f\u5206\u5e03\u306fscipy.stats.multivariate_normal\u3067\u5b9f\u88c5\u3055\u308c\u3066\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# \uff12\u6b21\u5143\u6b63\u898f\u5206\u5e03\n",
      "mu = array([1, 1]) # \u5e73\u5747\n",
      "S  = array([[1.0, -0.5],[-0.5, 2.0]]) # \u5206\u6563\u5171\u5206\u6563\u884c\u5217\n",
      "rv = stats.multivariate_normal(mu, S) # N(mu, S)\n",
      "\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "fig = figure()\n",
      "ax = Axes3D(fig)\n",
      "x, y = meshgrid(linspace(-1, 3), linspace(-2, 4))\n",
      "z = rv.pdf(transpose([x,y], (1,2,0)))\n",
      "ax.plot_wireframe(x, y, z)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<mpl_toolkits.mplot3d.art3d.Line3DCollection at 0x8aae250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8+fOZN29ek9u3M2PGDGbMmAHAG2+8wa233loU0QNX+EpKLoInyzLBYJBoNJq2SNoDmYIn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\ncvz4FOefHyAet6q49OhhMn9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ll/nZtk3immv87LKLzsiRKY44QkOSYN68GFdckWToUIP+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\nLVv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500alSiZxcRrHjrnJmjX9nBszxsbZswrFigkWLtQZNMhPz54G7dvbqVTJYtgwGYy/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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x82f8a10>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "axes().set_aspect('equal')\n",
      "contour(x, y, z)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<matplotlib.contour.QuadContourSet instance at 0x8de8e60>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vEevXJ5CRoa1dji1UuLE3bBjCwYNpuiLgokMhUeUqEoIL51Q02nLCC4uKVQxQ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x808d890>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u6307\u6570\u5206\u5e03\n",
      "\u5b9a\u6570 $\\lambda > 0$ \u306b\u5bfe\u3057\u3066 $x\\geq 0$ \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u5bc6\u5ea6\u95a2\u6570\u304c\n",
      "\n",
      "$$\\pi(x) = \\lambda e^{-\\lambda x} $$\n",
      "\n",
      "\u3067\u3042\u308b\u3082\u306e\u3092**\u6307\u6570\u5206\u5e03(exponential distribution)**\u3068\u547c\u3073\u3001$\\mathrm{Exp}(X|\\lambda)$ \u3068\u66f8\u304f\u3002\n",
      "$$\\mathrm{E}[X] = \\frac{1}{\\lambda},\\qquad\\mathrm{V}[X] = \\frac{1}{\\lambda^2}$$\n",
      "\n",
      "\u6307\u6570\u5206\u5e03\u306f\u30dd\u30a2\u30bd\u30f3\u5206\u5e03 $\\mathrm{Po}(X|\\lambda)$ \u306b\u5f93\u3046\u30a4\u30d9\u30f3\u30c8\u304c\u3001\u6b21\u306b\u767a\u751f\u3059\u308b\u307e\u3067\u306e\u5f85\u3061\u6642\u9593\u306e\u5206\u5e03\u3067\u3059\u3002scipy.stats.expon\u304c\u3053\u308c\u3092\u5b9f\u88c5\u3057\u3066\u3044\u307e\u3059\u3002$\\mathrm{Exp}(X|\\lambda)$ \u3092\u4f5c\u308b\u70ba\u306b\u306f,`scale`\u30d1\u30e9\u30e1\u30fc\u30bf\u306b$1/\\lambda$\u3092\u6e21\u3057\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 3)\n",
      "plot(x, stats.expon(scale=1.0/1).pdf(x), label='Exp(1)')\n",
      "plot(x, stats.expon(scale=1.0/2).pdf(x), label='Exp(2)')\n",
      "plot(x, stats.expon(scale=1.0/3).pdf(x), label='Exp(3)')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "<matplotlib.legend.Legend at 0x8cbb510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aL0WvV98EnTvDW2+ZV29N28rIL0fyVM+n+Eeff5h+XgkhhN2ktYwTaZoaNGTW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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x82eb4d0>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\u984c\n",
      "\u3042\u308b\u5546\u5e97\u306b\u306f\uff11\u6642\u9593\u3042\u305f\u308a\u5e73\u5747\u30673\u4eba\u304c\u6765\u5ba2\u3059\u308b\u3002\u6b21\u306e\u5ba2\u309230\u5206\u4ee5\u4e0a\u5f85\u305f\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u78ba\u7387\u306f\uff1f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rv = stats.expon(scale=1.0/3)\n",
      "print 'P(X >= 0.5) = 1 - P(X <= 0.5) =', 1-rv.cdf(0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X >= 0.5) = 1 - P(X <= 0.5) = 0.223130160148\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u5ba2\u3092\u5f85\u3061\u7d9a\u3051\u3066\u65e2\u306b2\u6642\u9593\u6765\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u6761\u4ef6\u4e0b\u3067\u3001\u3055\u3089\u306b30\u5206\u4ee5\u4e0a\u5f85\u305f\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u78ba\u7387\u306f\uff1f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'P(X >= 2.5 | X >= 2) = P(X >= 2.5 \u304b\u3064 X >= 2)/P(X >= 2) = P(X >= 2.5)/P(X >= 2) =', (1-rv.cdf(2.5))/(1-rv.cdf(2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(X >= 2.5 | X >= 2) = P(X >= 2.5 \u304b\u3064 X >= 2)/P(X >= 2) = P(X >= 2.5)/P(X >= 2) = 0.223130160148\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4eca\u5b9f\u9a13\u3057\u305f\uff12\u3064\u306e\u5024\u304c\u7b49\u3057\u3044\u4e8b\u306b\u6ce8\u76ee\u3057\u3066\u4e0b\u3055\u3044\u3002\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306b\u5f93\u3044\u767a\u751f\u3059\u308b\u4e8b\u8c61\u306b\u5bfe\u3057\u3066\u306f\u3001\u300c\u3082\u3046\u305a\u3063\u3068\u5ba2\u304c\u6765\u3066\u3044\u306a\u3044\u304b\u3089\u3001\u305d\u308d\u305d\u308d\u6765\u308b\u3060\u308d\u3046\u300d\u3068\u3044\u3046\u8003\u5bdf\u306f\u8aa4\u308a\u3067\u3042\u3063\u3066\u3001\u5e7e\u3089\u9577\u304f\u5f85\u3068\u3046\u304c\u6b8b\u308a\u6642\u9593\u306e\u78ba\u7387\u5206\u5e03\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002(\u30d9\u30a4\u30ba\u78ba\u7387\u8ad6\u7684\u306b\u306f\u3001\u300c\u3082\u3046\u305a\u3063\u3068\u5ba2\u304c\u6765\u3066\u3044\u306a\u3044\u304b\u3089\u3001\u5b9f\u306f $\\lambda$ \u306f\u601d\u3063\u3066\u3044\u305f\u3088\u308a\u5c0f\u3055\u3044\u306e\u3067\u306f\uff1f\u300d\u3068\u3044\u3046\u6539\u8a02\u306f\u3042\u308a\u3048\u307e\u3059\u3002)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u7121\u8a18\u61b6\u6027\n",
      "\u4eca\u306e\u4f8b\u3067\u898b\u305f\u6027\u8cea\u3092\u6307\u6570\u5206\u5e03\u306e**\u7121\u8a18\u61b6\u6027(memoryless)**\u3068\u547c\u3073\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u7121\u8a18\u61b6\u6027\u3011\n",
      "\n",
      "\u4efb\u610f\u306e $s,t > 0$ \u306b\u5bfe\u3057\u3066 $P(X > s+t | X > s) = P(X > t)$\n",
      "\n",
      "----\n",
      "\n",
      "\u6307\u6570\u5206\u5e03\u306f\u7121\u8a18\u61b6\u6027\u3092\u6301\u3064\u552f\u4e00\u306e\u5206\u5e03\u3067\u3042\u308b\u4e8b\u3092\u793a\u3059\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\n",
      "\n",
      "----\n",
      "\u3010\u8a3c\u660e\u3011\n",
      "\n",
      "\u4efb\u610f\u306e $s,t > 0$ \u306b\u5bfe\u3057\u3066 $P(X > s+t | X > s) = P(X > t)$\n",
      "\u3067\u3042\u308b\u3068\u3059\u308b\u3002\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3092 $F(X)$ \u3068\u3057\u3066 $G(X) = 1-F(X)$ \u3068\u7f6e\u304f\u3068\u3001\n",
      "$$ P(X > t) = 1 - P(X >= t) = G(t),\\quad P(X > s+t | X > s) = \\frac{P(X > s+t, X > s)}{P(X > s)} = \\frac{P(X > s+t)}{P(X > s)} = \\frac{G(s+t)}{G(s)}$$\n",
      "\u3067\u3042\u308b\u304b\u3089\u3001\n",
      "\n",
      "$$ G(s+t) = G(s)G(t)$$\n",
      "\n",
      "\u304c\u6210\u308a\u7acb\u3064\u3002\u5f93\u3063\u3066\n",
      "\n",
      "$$ \\frac{G(s+t)-G(s)}{t} = G(s)\\frac{G(t)-G(0)}{t}\\qquad(\\because G(0)=1-F(0)=1)$$\n",
      "\n",
      "\u3067\u3042\u308b\u306e\u3067\u4e21\u8fba\u306e $t\\rightarrow 0$ \u306e\u6975\u9650\u3092\u53d6\u308b\u3068\n",
      "\n",
      "$$ G'(s) = G(s)G'(0)$$\n",
      "\n",
      "\u304c\u6210\u308a\u7acb\u3064\u3002 $G(x)$ \u306f\u5358\u8abf\u6e1b\u5c11\u95a2\u6570($F(x)$ \u304c\u5358\u8abf\u5897\u52a0)\u306a\u306e\u3067 $G'(0) = -\\lambda\\quad(\\lambda > 0)$ \u3068\u304a\u304f\u3068$ G'(x) = -\\lambda G(x)$\u3088\u308a\n",
      "\n",
      "$$ G(x) = \\exp(-\\lambda x)\\qquad (\\because G(0) = 1)$$\n",
      "\u3067\u3042\u308b\u3002\u5f93\u3063\u3066\n",
      "\n",
      "$$ F(x) = 1-\\exp(-\\lambda x)$$\n",
      "\n",
      "\u3067\u3042\u308b\u304b\u3089\u3001\n",
      "\n",
      "$$\\pi(x) = \\frac{\\mathrm{d} F}{\\mathrm{d} x} = \\lambda\\exp(-\\lambda x)$$\n",
      "\n",
      "\u3068\u306a\u308b\u3002\n",
      "\n",
      "----\n",
      "\n",
      "\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306e\u89b3\u70b9\u304b\u3089\u306f\u300c\u5e73\u5747\u5024\u304c $1/\\lambda$ \u3068\u3044\u3046\u6761\u4ef6\u3092\u6e80\u305f\u3057\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u3092\u6700\u5927\u306b\u3059\u308b\u78ba\u7387\u5206\u5e03\u304c $\\mathrm{Exp}(X|\\lambda)$ \u3067\u3042\u308b\u300d\u4e8b\u3092\u793a\u3059\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\u3084\u3063\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u5e7e\u4f55\u5206\u5e03\u3068\u306e\u95a2\u4fc2\n",
      "\u6307\u6570\u5206\u5e03\u306f\u5e7e\u4f55\u5206\u5e03\u306e\u9023\u7d9a\u7248\u3067\u3042\u308b\u3068\u8003\u3048\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002\n",
      "- \u30a8\u30d9\u30f3\u30c8\u304c\u521d\u3081\u3066\u751f\u3058\u308b\u307e\u3067\u306e\u8a66\u884c\u56de\u6570\u306e\u5206\u5e03:\u5e7e\u4f55\u5206\u5e03 $\\mathrm{Geom}(X|p)$\n",
      "- \u30a4\u30d9\u30f3\u30c8\u304c\u521d\u3081\u3066\u751f\u3058\u308b\u307e\u3067\u306e\u6642\u9593\u306e\u5206\u5e03: \u6307\u6570\u5206\u5e03 $\\mathrm{Exp}(X|\\lambda)$\n",
      "\n",
      "\u3042\u308b\u30a4\u30d9\u30f3\u30c8\u306e\u751f\u3058\u308b\u78ba\u7387\u304c $p$ \u3067\u3042\u308b\u3068\u3044\u3046\u306e\u306f\u3001\u4e00\u56de\u3042\u305f\u308a\u5e73\u5747 $p$ \u56de\u3068\u3044\u3046\u610f\u5473\u306a\u306e\u3067\u3001\n",
      "\n",
      "$$ \\mathrm{Geom}(X|p) \\approx\\mathrm{Exp}\\left(X\\middle|p\\right)$$\n",
      "\n",
      "\u3068\u8fd1\u4f3c\u51fa\u6765\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p = 0.1\n",
      "geom  = stats.geom(p)\n",
      "expon = stats.expon(scale = 1/p)\n",
      "x = arange(1, 30)\n",
      "bar(x, geom.pmf(x), alpha=0.3, align='center', width=0.5, color='blue', label='Geom(%f)' % p)\n",
      "x = linspace(0, 30)\n",
      "plot(x, expon.pdf(x), color='red', label='Exp(%f)' % p)\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "<matplotlib.legend.Legend at 0x8cc7050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aRo/W27Yi4qBqHE9Srx6sXQvx8dCqFQEnjlkdkYi4CCV7T1O8OMybB5060en9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\niIiI5L3/B0cpO7S9eSBaAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8cc75d0>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u30ac\u30f3\u30de\u5206\u5e03\n",
      "\u5b9a\u6570 $\\lambda,k > 0$ \u306b\u5bfe\u3057\u3066 $x > 0$ \u4e0a\u3067\u306e\u5bc6\u5ea6\u95a2\u6570\u304c\n",
      "$$ \\pi(x) \\approx x^{k-1}e^{-\\lambda x}$$\n",
      "\u3068\u8868\u3055\u308c\u308b\u78ba\u7387\u5206\u5e03\u3092 **\u30ac\u30f3\u30de\u5206\u5e03(gamma distribution)** \u3068\u547c\u3073\uff0c$\\mathrm{Gamma}(X| k, \\lambda)$ \u3068\u66f8\u304d\u307e\u3059\u3002\u30c6\u30ad\u30b9\u30c8\u306b\u3088\u3063\u3066\u306f$\\theta=1/\\lambda$\u3092\u7528\u3044\u3066 $\\mathrm{Ga}(X|k,\\theta)$ \u3068\u66f8\u304f\u5834\u5408\u3082\u3042\u308b\u306e\u3067\u6ce8\u610f\u3057\u3066\u4e0b\u3055\u3044\u3002\u3053\u306e\u30c6\u30ad\u30b9\u30c8\u3067\u306f $\\lambda$ \u3092\u7528\u3044\u305f\u8a18\u8ff0\u306b\u7d71\u4e00\u3057\u307e\u3059\u3002\n",
      "\u30ac\u30f3\u30de\u5206\u5e03\u306f\u6307\u6570\u5206\u5e03\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3067\u3042\u308a $\\mathrm{Exp}(X|\\lambda) = \\mathrm{Ga}(X|1, \\lambda)$ \u306e\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002\n",
      "$$\\mathrm{E}[X] = \\frac{k}{\\lambda},\\qquad\\mathrm{V}[X]=\\frac{k}{\\lambda^2}$$\n",
      "\u30ac\u30f3\u30de\u5206\u5e03\u306f $\\mathrm{Po}(\\lambda)$ \u306b\u5f93\u3046\u30a4\u30d9\u30f3\u30c8\u304c $X$ \u56de(\u6574\u6570\u3068\u306f\u9650\u3089\u306a\u3044)\u751f\u3058\u308b\u307e\u3067\u306e\u5f85\u3061\u6642\u9593\u3092\u8868\u3057\u3066\u3044\u308b\u3068\u89e3\u91c8\u3059\u308b\u4e8b\u304c\u51fa\u6765\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4ee5\u4e0b\u306f $k$ \u3092\u56fa\u5b9a\u3057\u305f\u5834\u5408\u306e\u30ac\u30f3\u30de\u5206\u5e03\u306e\u69d8\u5b50\u3067\u3059\u3002$\\lambda$ \u304c\u5897\u3048\u308b\u307b\u3069(\u767a\u751f\u983b\u5ea6\u304c\u5897\u3048\u308b\u307b\u3069)\u5f85\u3061\u6642\u9593\u306f\u5c0f\u3055\u304f\u306a\u308b\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k = 3\n",
      "x = linspace(0, 5)\n",
      "plot(x, stats.gamma(k, scale=1.0/1).pdf(x), label='Ga(3, 1)')\n",
      "plot(x, stats.gamma(k, scale=1.0/2).pdf(x), label='Ga(3, 2)')\n",
      "plot(x, stats.gamma(k, scale=1.0/3).pdf(x), label='GA(3, 3)')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "<matplotlib.legend.Legend at 0x942bfd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3Kc+qgat4ac1L7L6420rBCSGsxXESuVJWSeTT90xndNPRqSuMOb6xY2HaNLOG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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8dcba50>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4ee5\u4e0b\u306f $\\lambda$ \u3092\u56fa\u5b9a\u3057\u305f\u5834\u5408\u3067\u3059\u3002$k$\u56de\u751f\u3058\u308b\u307e\u3067\u306e\u6642\u9593\u306f\u5f53\u7136\u9577\u304f\u306a\u3063\u3066\u3044\u304d\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lam = 3\n",
      "x = linspace(0, 3)\n",
      "plot(x, stats.gamma(1, scale=1.0/lam).pdf(x), label='Ga(1, 3)')\n",
      "plot(x, stats.gamma(2, scale=1.0/lam).pdf(x), label='Ga(2, 3)')\n",
      "plot(x, stats.gamma(3, scale=1.0/lam).pdf(x), label='GA(3, 3)')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "<matplotlib.legend.Legend at 0x96d01d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7zYLFMl1CAnTvDr/8otM05Vy4ALNn69G2O3SAZ57RQdbZuVbHupR/ifHfjych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\nhBBCCCFEffT/AXaTzlzdRbvVAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8320550>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\uff11\u65e5\u5f53\u305f\u308a\u5e73\u57475\u4eba\u306e\u65b0\u898f\u767b\u9332\u304c\u3042\u308b\u30b5\u30fc\u30d3\u30b9\u3092\u904b\u55b6\u3057\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002\u534a\u5e74\u4ee5\u5185\u306b1000\u4eba\u306e\u65b0\u898f\u30e6\u30fc\u30b6\u3092\u5f97\u308b\u78ba\u7387\u306f\uff1f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print stats.gamma(1000.0, scale = 1/5.0).cdf(365.0/2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.00224534274454\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u3068\u306e\u95a2\u4fc2\n",
      "\u6307\u6570\u5206\u5e03\u304c\u5e7e\u4f55\u5206\u5e03\u306e\u9023\u7d9a\u7248\u3068\u307f\u306a\u305b\u305f\u3088\u3046\u306b\u3001\u8ca0\u306e\u4e8c\u9805\u5206\u5e03\u306e\u9023\u7d9a\u7248\u304c\u30ac\u30f3\u30de\u5206\u5e03\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u9006\u30ac\u30f3\u30de\u5206\u5e03\n",
      "\n",
      "$X \\sim \\mathrm{Gamma}(X|k,\\lambda)$ \u306e\u6642\u306b $1/X$ \u304c\u5f93\u3046\u78ba\u7387\u5206\u5e03\u3092**\u9006\u30ac\u30f3\u30de\u5206\u5e03(inverse gamma distribution)**\u3068\u547c\u3073 $\\mathrm{InvGamma}(X|k,\\lambda)$ \u3068\u66f8\u304d\u307e\u3059\u3002\u5f93\u3063\u3066\u5909\u6570\u5909\u63db\u306e\u516c\u5f0f\u3092\u7528\u3044\u308c\u3070\u305d\u306e\u5bc6\u5ea6\u95a2\u6570\u306f\n",
      "\n",
      "$$\\pi(x) \\propto x^{-k-1}e^{-\\lambda/x}\\qquad(x \\geq 0)$$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u5e73\u5747\u306f\n",
      "\n",
      "$$\\mathrm{E}[X] = \\frac{\\lambda}{k-1}\\quad(k > 1),\\qquad \\mathrm{V}[X] = \\frac{\\lambda^2}{(k-1)^2(k-2)^2}\\quad(k>2)$$\n",
      "\n",
      "\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 3)\n",
      "plot(x, stats.invgamma(1, scale=1/1.0).pdf(x), label='InvGamma(1,1)')\n",
      "plot(x, stats.invgamma(1, scale=1/2.0).pdf(x), label='InvGamma(1,2)')\n",
      "plot(x, stats.invgamma(2, scale=1/1.0).pdf(x), label='InvGamma(2,1)')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "<matplotlib.legend.Legend at 0x9f3d4d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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glJGqJ+4V5ZYB5XeXMMCCIDggVU/cK8otAzBsGISHq3sKgiA4EFVT3CvCLQMqVvzw4bKg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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9f15e90>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u30ac\u30f3\u30de\u5206\u5e03\u306f\u30dd\u30a2\u30bd\u30f3\u7684\u306b\u767a\u751f\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u304c $k$ \u56de\u751f\u3058\u308b\u307e\u3067\u306e\u5f85\u3061\u6642\u9593\u306e\u5206\u5e03\u3068\u3044\u3046\u89e3\u91c8\u304c\u53ef\u80fd\u3067\u3057\u305f\u304c\u3001\u9006\u30ac\u30f3\u30de\u5206\u5e03\u306b\u5bfe\u3059\u308b\u5206\u304b\u308a\u3084\u3059\u3044\u89e3\u91c8\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5f8c\u306e\u56de\u306b\u8aac\u660e\u3057\u307e\u3059\u304c\u3001\u9006\u30ac\u30f3\u30de\u5206\u5e03\u306f\u30d9\u30a4\u30ba\u7d71\u8a08\u306b\u304a\u3044\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u4e8b\u524d\u5206\u5e03\u3092\u8868\u73fe\u3059\u308b\u76ee\u7684\u3067\u4e3b\u306b\u4f7f\u308f\u308c\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u5e73\u5747\u30fb\u5206\u6563\u306e\u5b58\u5728\u3057\u306a\u3044\u5206\u5e03\n",
      "\u3068\u3053\u308d\u3067\u3001\u9006\u30ac\u30f3\u30de\u5206\u5e03\u306e\u5e73\u5747\u30fb\u5206\u6563\u306f $k\\leq 1$ \u3084 $k\\leq 2$\u306e\u6642\u306b\u306f\u5b58\u5728\u3057\u306a\u3044\u3068\u3044\u3046\u4e8b\u306b\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u3088\u3046\u306a\u5206\u5e03\u3067\u306f\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\u3084\u5f8c\u306b\u8ff0\u3079\u308b\u5927\u6570\u306e\u6cd5\u5247\u306a\u3069\u3001\u7d71\u8a08\u5b66\u306e\u91cd\u8981\u306a\u5b9a\u7406\u304c\u6210\u7acb\u3057\u307e\u305b\u3093\u306e\u3067\u6ce8\u610f\u3057\u3066\u4e0b\u3055\u3044\u3002\n",
      "\n",
      "\u4f8b\u3048\u3070\u3001$X_1,\\ldots,X_n$ \u304ci.i.d. \u306a\u3089\u3070\u6a19\u672c\u5e73\u5747 $\\overline{X}$ \u306e\u5024\u306f $n\\rightarrow\\infty$ \u306e\u6642\u5206\u5e03\u306e\u5e73\u5747\u5024\u306b\u53ce\u675f\u3057\u307e\u3059(\u5927\u6570\u306e\u6cd5\u5247)\u3002\u4f8b\u3048\u3070 $\\mathrm{Bern}(p)$ \u306b\u5f93\u3046\u8a66\u884c\u3092\u591a\u6570\u884c\u3048\u3070\u3001\u6a19\u672c\u306e\u5e73\u5747\u5024\u306f $p$ \u306b\u53ce\u675f\u3057\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Bern(0.3) \u306e\u5834\u5408 (\u6a19\u672c\u5e73\u5747\u306f0.3\u306b\u8fd1\u3065\u3044\u3066\u3044\u304f\u306f\u305a)\n",
      "N = 1000\n",
      "samples = []\n",
      "s = 0.0 # \u6a19\u672c\u306e\u548c\n",
      "for k in range(N):\n",
      "    x = stats.bernoulli(0.3).rvs(1) # \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n",
      "    s += x                  # \u548c\u3092\u66f4\u65b0\u3057\u3066 \n",
      "    samples.append(s/(k+1)) # k+1\u3067\u306e\u6a19\u672c\u5e73\u5747\u3092\u8ffd\u52a0\n",
      "plot(samples)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 46,
       "text": [
        "[<matplotlib.lines.Line2D at 0xa922c10>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Rrit10R/4NtYYOh77rFwbt44rdZFIstfeIm0d9luwAcuIQhrujbJVPhb0/4t1\n44Dtrfv41/tiIQiN66jAX5YNzgMuBTYCTwGfxerExboo9y8l/u1nsND/N+7VxQjg/7AfUKwDnsO6\nfF2si4h0PhPl/vKCuOXtWid52Le/ioAOuDFAmwP8Duu+iDWLaN/bHTQegOmAHeqvJ7VvNh9uLiTa\nZ+9qXbwODPSvF2P14GJdDMfOVOuEvaa5wLdwqy6KaDxAm+5rX4qd0ZXDITBAC4m/kJXNzsf6p1di\n3RcrsH9CL2ygMtGpVd/H6qcUuDiThc2gC4mejeNqXQzHWvarsNZsd9yti6lET72cix0Nu1IXT2Fj\nFQewMc3raNlrj5x6WQY81OalFhERERERERERERERERERERERERERERERERE5nPw/OqTq4QLpvS4A\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa6ece50>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4e00\u65b9\u3067\u3001\u5e73\u5747\u306e\u5b58\u5728\u3057\u306a\u3044\u5206\u5e03\u3067\u306f\u3053\u308c\u304c\u6210\u308a\u7acb\u3061\u307e\u305b\u3093\u3002\u4f8b\u3068\u3057\u3066 $\\mathrm{InvGamma}(1, 2)$ \u304b\u3089\u306e\u6a19\u672c\u5e73\u5747\u306e\u69d8\u5b50\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# InvGamma(1,2)\u306e\u5834\u5408. \u5e73\u5747\u304c\u5b58\u5728\u3057\u306a\u3044\u306e\u3067\u53ce\u675f\u3057\u306a\u3044\u306f\u305a\u3002\n",
      "N = 1000\n",
      "samples = []\n",
      "s = 0.0 # \u6a19\u672c\u306e\u548c\n",
      "for k in range(N):\n",
      "    x = stats.invgamma(1, scale=1/2.0).rvs(1) # \u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\n",
      "    s += x                  # \u548c\u3092\u66f4\u65b0\u3057\u3066 \n",
      "    samples.append(s/(k+1)) # k+1\u3067\u306e\u6a19\u672c\u5e73\u5747\u3092\u8ffd\u52a0\n",
      "plot(samples)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 50,
       "text": [
        "[<matplotlib.lines.Line2D at 0xb2cfe50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qVkREfE49chERn1MgFxHxOQVyERGfUyAXEfE5newUEfE5VwJ5aakbaxERkUS4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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xab5da90>"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4ee5\u5f8c\u3001\u4ed6\u306b\u3082\u5e73\u5747\u3084\u5206\u6563\u306e\u5b58\u5728\u3057\u306a\u3044\u5206\u5e03\u304c\u8907\u6570\u767b\u5834\u3057\u307e\u3059\u3002\u305d\u308c\u3089\u306b\u5bfe\u3057\u3066\u306f\u901a\u5e38\u306e\u7d71\u8a08\u5206\u6790\u624b\u6cd5\u304c\u4f7f\u3048\u306a\u3044\u306e\u3067\u3001\u5206\u5e03\u306e\u540d\u524d\u306f\u899a\u3048\u3066\u304a\u304f\u3068\u826f\u3044\u3068\u601d\u3044\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u30d9\u30fc\u30bf\u5206\u5e03\n",
      "\n",
      "\u5b9a\u6570 $\\alpha,\\beta>0$ \u306b\u5bfe\u3057\u3066\u533a\u9593 $[0,1]$ \u3067\u5b9a\u7fa9\u3055\u308c\u305f\u5bc6\u5ea6\u95a2\u6570\u304c\n",
      "\n",
      "$$\\pi(x)\\propto x^{\\alpha-1}(1-x)^{\\beta -1}$$\n",
      "\n",
      "\u3068\u306a\u308b\u3082\u306e\u3092**\u30d9\u30fc\u30bf\u5206\u5e03(beta distribution)**\u3068\u547c\u3073 $\\mathrm{Beta}(X|\\alpha,\\beta)$ \u3068\u66f8\u304d\u307e\u3059\u3002\u6a19\u6e96\u4e00\u69d8\u5206\u5e03\u306f\u30d9\u30fc\u30bf\u5206\u5e03\u306e\u7279\u5225\u306a\u5834\u5408\u3067\u3042\u308a\u3001$\\mathrm{U}(X)=\\mathrm{Beta}(X|1,1)$\u3067\u3059\u3002\n",
      "$$\\mathrm{E}[X] = \\frac{\\alpha}{\\alpha+\\beta},\\qquad\\mathrm{V}[X]=\\frac{\\alpha\\beta}{(\\alpha+\\beta)^2(\\alpha+\\beta+1)}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 1)\n",
      "plot(x, stats.beta(1, 1).pdf(x), label='Beta(1,1)')\n",
      "plot(x, stats.beta(2, 2).pdf(x), label='Beta(2,2)')\n",
      "plot(x, stats.beta(3, 4).pdf(x), label='Beta(3,4)')\n",
      "plot(x, stats.beta(0.5, 2).pdf(x), label='Beta(1/2,2)')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "<matplotlib.legend.Legend at 0xb3f1290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9u61b1XjFxMCnn6p/GDdsgA4d1OdSg1TYkSZ3IbI6R7VaRh85wj1BQbwZE4Or\nPXQ57N0Ljz2m3pa9bJk6OkRYV0ICvPCCesa9ZAn062frFolGREaP3KDckhIeTkrCYDSyqlMn292E\nU1ICr7wC//oXLF6szqchbEdR1Nvj//53NbTfeEOdP1yIGySjR26Qxs2NdV27cqu/P7fs388BW1yM\nOnIEevdW+1YPHJDAtgdOTjBmjDpBVbt2avfUyy+rXVdC2ICEdiUuTk68FhPDopgYhhw6xKfp6dYp\nFmw0wltvqbecT5miTpkaEdHw+xXm8/FRw3rfPrVIQ8eO6vS2jeBTpnAs0j1Sg0OFhYw5doyO3t4s\nj40luKG6S7Kz1cmc8vPVeUNat26Y/QjLio9Xx3YHB6vXHGJjbd0i4WCkT7sB6MrKmHPuHJ9mZLCs\nXTvuDQ627A5+/13tAhkzRu3HbiqzENZBqbGUAn0B+fr8KouuVIe+TI++VF/lq6HMUOO2nHDC3cUd\nD1cPPFw8qnz1dvPG38O/yuLr7ouz03U+jJaWwvvvw8KF6o1OL74IUptUmElCuwFtv3KF/zt+nD7+\n/ixp2xbNjYaroqjTpi5apM5EN2KEZRrqAIyKkYzCDC7lXyKlIIW0gjSyirLI0maRXZxNljbL9DxP\nl4ehzICfh1+VMPVz98PLzcsUuO7OV4PY3cW9xhJzRsWIocxwNegrhX1RSVGVPw4FhgIKDYV4u3mj\n8dQQ7BNMsHfw1a/lj8N9w2ld6EabBUtxP5KE0z//qd6hKkQtJLQbmLasjBfOnOG7rCw+at+eYfUd\ngpebC+PGQWqqOtlTdLRF22lrpcZSLl65SHJuMsmXkzmTe4ZzV85xKf8Sl/IvkVaQhsZLQ6R/JJH+\nkYT5hF0biOVfNV4avFy9bFbn06gYKTQUcrn4cpU/JtlF2WQVZZGpzSStMM30vcUd1bJkvcKpthq+\nndifZjGdaaNpQ4wmhjbN2hDuGy41S4WJhLaV/JybyxPHjzMwMJDXY2IIr8ukU3v3qnUNR4yAN98E\nB54iNqcoh2NZx0zL8ZzjJF9O5mL+RUJ9QmnTrI0psKIDo4nyjyLSP5IIvwg8XB14oq7rKDQUkpp+\nGvdFbxL2xVq2PN6fVf0CSb5yluTcZAoNhbQObE2bZm3o2LwjnYI70Sm4Ex2ad8DX3dfWzRdWJqFt\nRQWlpbxy/jz/SUtjZsuWTIuMxL22G3JWroQZM9SLVvffb52GWkBxSTFHMo9wIP0AiemJppDWl+nV\n0Gl+NXg2yxvGAAAcIUlEQVTaNmtLdGB0ow3lOjl6VJ1B0NUVPvoIOnSgQF/AmdwznL58mqTsJI5l\nHSMpO4kT2ScI9gmmU3AnOgd3pntYd3qE9aB98/a4Orva+jsRDURC2wZOFhXx7OnTnCwu5r22bRle\nXZdJaSnMnKlOA/rDD+qET3aqQF/AvrR97E/bz4H0AxxIO0BybjKxQbH0COtB97DudA7uTKfgTkT4\nRchH/dqUlal/pOfPh+nT1Rt0qvl0VWYs41zeOY5lHeNw5mES0xM5kH6A1IJUOgd3pkdYD3qE96BX\neC+6hXXD3cVxP6GJqyS0bejHnByeOX2atl5evNu2LbHe3uqKvDx1dEhpqdp/bUcT7hsVI8ezj7Pz\n0k52XdrFzpSdnL58mm6h3egV3ks92wvvQefgznLmfKMuXFCr5Vy6pF54vvVWs95WoC/gYMZBDqSp\nn3L2pO4hOTeZ7mHd6d2iN30i+9Ansg9R/lHyB9QBSWjbmMFoZMmlS7x+4QJjQkOZVVJC+L33wtCh\n8Pbb6sdkG9KX6tmTuoet57ey9fxWdl7aSXPv5vSJ7GMKADmLa0AVt8M/88zVIZ4+PnXeTIG+gL2p\ne9mVsoudl3ay89JOnJ2c6RvVl4GtBjIweiBdQrpcf6iisAsS2nYi02BgUUICn+h0/F9ZGTOHD7dJ\nTcrikmJ2XtpJwvkEtp7fyp7UPbQPas+AVgMY2GogfaP6Euxj4XHnonbZ2Wpw//67etZ9g+XhFEXh\n/JXzbLuwjYRzCWy9sJXsomz6tezHgJYDGBg9kB5hPXBxdrHQNyAsRULbHigKvPMOvP02qV9/zWuh\noXyRkcHEiAhmREUR1IA3zyiKwqGMQ2w+s5lNyZvYcWkHnYM7m86+bo+6nQDPgAbbv6ijdevULpMR\nI9Tx+v7+Ftt0WkEaW89vJeF8AgnnE0grSGNwzGDuirmLIW2GEB0YbbF9ifqT0La10lJ1zusdO9Rf\nyPKZ4C7odCw8f55vsrJ4skULpkVGWiy8M7WZbDy9kU1nNrE5eTN+Hn6mX8xB0YMkpO1dXp46omjz\nZrUq0Z/+1CC7SS1IZcuZLWxK3sTmM5sJ8Agw/T8ZHDNYhhvaiIS2LRUUqOOvFUW94FjNWdPZ4mIW\nnj/Pt9nZjAkJ4ZnISNpWXLA0U8XZ9LqT61h7ci3Hs48zOGYwQ2KGcFebu4jRxFjqOxLWtHkzTJgA\nd9yhXv/QaBpsV0bFyOGMw2xK3sTG5I3sStnF7VG3MyJ2BPfE3kOrwFYNtm9RlYS2rVy6BPfco06p\nunRprfOHpOn1LE1J4cO0NAYEBDAjKorbAmo+I9aX6vnl7C+sPbmWdSfX4ebiZvoFG9BqgFw4bCwK\nCtSCC2vWwPLlVpvaIF+fz6bkTaw7uY4fT/1ImG8Y98Tew4jYEfSO7C0XNBuQhLYtJCaqv1xTp8Lz\nz9epIrq2rIyP09J459Ilwt3deS4qipFBQbg6O1NcUsyG0xtYnbSa9afW0zm4MyPbj2RE7Ag6NO8g\nw7sas/h4eOIJuP12eO89qw4TLTOWsTtlN2tPruWHEz+Qq8vlzx3+zP2d7qdfy35yMdPCJLSt7aef\n1HJg//yn2jVST2WKwndZWbx18TyntPmEFezjwvHl3Bocw/0d7+fejvcS5htmwYYLu6fVqjMGrl6t\n3pwzapRNmnE8+zirj63mm6RvSCtIY3SH0dzf6X4GthqIm4vMSHmjGjK0/wvcDWQCXatZ3/RC+8MP\nYc4c+PZb6Nu33psxlBnYcHoDnx/+nA2nN9Cl9UjcI+8j0RjEII2GyRER3KnR4Cxn1k3T1q0wfrza\n9bZkiU3rhCZfTmZ10mq+OfYNZ/PO8kCnBxjbdSy3Rd0mXSj11JCh3R8oBFbS1ENbUWDuXPjiC/VM\nu127Om/CqBj57fxvfHH4C1YnraZTcCce7vowD3R6gCBv9ZeysLSULzMzWZ6aypXSUiaEh/NoWBgt\n6jI5lWgciorgH/+AVavUayZ//rOtW8TZ3LN8eeRLPj/8OVqDloe7PszDXR+mS0gXWzfNoTR090g0\nsJamHNqlpeq42oMH1SF9oaF1evvx7ON8kvgJXxz+Ao2Xhoe7PMyYrmNoGdCyxvcoisLeggI+Skvj\nm6wsbvbz47HQUO4NDsbHRfoXm5Rt29Sz7h491PC2dEGOeqgYzfT54c/58siXNPNqxiNdH+HRbo9K\nl54ZJLQbklYLf/mLGtzffAO+5o1rzdfns+rIKv6b+F/O5Z3jsZse49Fuj9brjKS4rIy1OTmsTE9n\ne34+o4KCeCwsjLjAQOk+aSqKi9VuuU8/hcWL1WspdvKzr/gEufLgSr49/i39W/ZnXPdx3B17t4xw\nqoGEdkPJylKH9HXooN52XMuQPqNiJOFcAh8nfswPJ37gjtZ3ML7HeIa2HWqxaTYzDAa+zMhgRUYG\nWQYDD4SE8GBwML39/SXAm4Jdu9RCGh06qBcqw+zrrLbQUMj/jv6PjxM/5kTOCcZ2Hcv4HuOl++QP\nbBraMLfS07jyxfFFc5aN/IlvuJ9/sJDrHi7vLOjxMfT6AEq84cB4ODwWtCEN28hWWhiYBYMywasM\nEoIhPgSS/K7fXuHQPNAxh5d5gv/wLO/wBQ9jlz/vZqeg+yfQfQXkR8LeyXDkL1DqZeuW2UB8+VJh\nPsiZtgUdOKCeYb/4onp7ejUURWH7xe38a++/WHdyHaM7jGbyzZPp3aK3TcZSH9Vq+V9mJquysigq\nK+PPwcGMCgqiX0AArrUVaRCOad8+9ay7VSv1ppzISFu3qFqlxlJ+OvUTy/cuZ3fKbh7r9hiTek2i\nffP2tm6azTTkmfaXwEAgCHXY3xzg40rrG19o//yzOn3m8uVw333XrM7X5/PZoc9Yvnc5hjIDk3tN\n5vHuj9PMyz7my1YUhSNaLd9lZ7MmO5vzOh3Dg4IY1bw5f9Jo8LXxNLHCwgwGeP11tTL8ggUwcSLY\n8R/ps7ln+XDfh/w38b90CenC5F6TGd1hdJMb+y0311jKqlXqHY7/+x8MHFhl1enLp3l/1/t8dvgz\nBrcezJSbpxAXHWf3dyhe1On4ISeHNdnZ7MzPp39AAHcHBTGsWTNaezXFj6mNVEWJM3d3tcRZbKyt\nW3RdhjID3yV9x/K9yzl9+TRP3vIkE3tNNA19bewktC1hyRJ44w348Ue46SZAPWv95ewvLN61mB2X\ndjCh5wT+dsvfiPS3z4+htblSWspPOTn8ePkyGy5fppmrK8PKA3xAQACeMpTQsZWVqXfpvvyyOoPg\nc8/VevHcHhxMP8jiXYv57vh3PNDpAZ7u/XSjv3ApoX0jFAVmzVLvcNy4EaKjKS4p5vPDn7N412KM\nipFpvafxyE2P4O1Wt5n57JlRUdhfUMBPly/z0+XLHNFqGRAQwJBmzbhTo6Gjt7fdf4oQNTh3DiZN\nUkc/ffQR9Opl6xaZJVObyQd7P2DZ3mV0Du7M9D7TGd5ueKO861JCu75KStQ+wGPHYP16cn1cWLZn\nGe/vfp9eEb2Y3ns6d8bc2STC63JJCZtzc9mSm8vmy5cxKAp3ajQM1mgYHBhIpKenrZso6kJR1DHd\nf/+7Wqt0wQLw87N1q8xiKDPw9dGveXfnuxSVFPF83+cZ23Vso6pXKqFdHxU3zRiNXPr3u7xz+AM+\nSfyEke1HMqPvjEb/8ex6FEXhjE7HlvIQ/yU3l2A3NwZpNAwMCGBgYCDhclu9Y8jOVmeh3LJFvVg5\nerStW2S2iu7JN35/gyOZR5jeezqTbp6Ev4flKv3YioR2XZXfNJMbHcZzD/jzffJ6xnUfx/Q+04kK\niLJ16+yOUVFILCwkIS+P+Lw8frtyhWA3N+ICAxlYvsjcKHYuPl6diqFDBzW8oxzr/3lieiJvbH+D\njckbmdBzAtN6TyPcL9zWzao3Ce26SE5Gd+cgfujuxdN983i6zzSm3DwFjVfDVQxpbMoUhcOFhSRc\nuUJCXh5b8/Lwc3Xldn9/bg8I4PaAADr7+ODSBLqVHIper9akXLIEXnpJvQfBwYaAns09y7s73+Wz\nQ58xpssYZvabed05fOyVhLaZDq/7LxGP/o03B3sR8fx8JvScgJebDHu7UYqicKKoiG1XrrA9P5/t\nV66QaTBwW0AAt/v708ffn1v8/QlwsIBotE6cgL/9Tf3EuXQpDBhg6xbVWaY2k3d2vMNH+z/izx3+\nzIv9X3SoknsS2rX47fxvbFzyNM98cIjd8ycyaNq7eLrKhbWGlGEw8PuVK/yen8+u/Hz2FxQQ7elJ\nn/IQ7+PvT0c5G7cdRVEnQHvuOTW033gDIiJs3ao6yynK4b2d77F873Luib2HWf1nERtk32PUQUK7\nRtsubGP2r7PpveEIczYbcPt+LW79HO+sojEoMRo5rNWyMz+fnfn57MjPJ91goKevL7f4+XGLvz+3\n+PnR2tOzSYzWsRuFhfDqq2pxjxdegKefVm/QcTB5ujyW7FrC+7vfZ0ibIcwbOI92QXWf895aJLT/\nYE/KHmb/OpsT2cf59nh3um86hNOGDXZ/l1hTc7mkhL0FBewtKGBPQQF78vMpNhq52c+Pm/386Onn\nR09fX6IlyBveyZMwbZo6xnvJErjrLlu3qF7y9fks2bWExbsWM6r9KGYPmG2XVeYltMsdzjjM7F9n\nszd1L3P6zOSJ5btwSTquFi6wsyksRfXS9Hr2FBSwv6CA/YWF7C8oQGs00tPXlx6+vvT086O7ry+x\nXl4yEZalKQqsXQvPPAOdOqldJh072rpV9ZJbnMvbO95m+d7ljOkyhln9ZxHhZz/dP00+tE/mnGRu\n/Fx+PfsrM2+fyeTo+/F68GEICVFvMPBuPHcyNkUZBgMHKoV4YmEhaQYDnX186ObrS3dfX7r5+HCT\nry/+crHzxun16u3wr70GDzwA8+apv0sOKEubxaLti/g48WPGdx/PzH4zae7d3NbNarqhnVaQxvyE\n+axOWs0zfZ7h6d5P45t8UZ1W9cEHYeFCu57xTNRfQWkph7RaDhYWklhYyMHCQo5otYS4u3OTjw9d\nfXzo6utLVx8fOSuvr5wceOUV9cTnuedg+nRw0EnGUvJTWPjbQr4++jXP9HmGZ257xqbTUjS50C7Q\nF/Dm72/yzz3/ZFz3cczqP0udGnXLFnj4YXUs6rhxVm+XsK0yRSG5uJjDWi2HCgs5rNVyWKslRa8n\n1suLLj4+dK60tPb0lGo/5jh9Wr1IuWePeiI0Zgw46ORipy+f5h+//INtF7YxP24+/9f9/yxWVaou\nmkxol5SV8OG+D1mwdQF3tbmLBYMWEB0Yra784AO1WvqqVddMqyqaNm1ZGce0Wo5qtRwtKuJI+ePL\nJSV08Pamk48Pnby96ejjQ0dvb2I8PeXMvDrbtsHMmZCXB/Pnq9XhHfQ47U7Zzd83/51MbSav3/k6\nI2JHWPVid6MPbUVR+DbpW174+QViNDEsunMR3cO6qytLS9VJcdavVy84trPfYT7CvlwpLeWYVsux\noiKStFqSioo4VlREusFAWy8vOnp709Hbmw7e3rT39ibWy0uKSCiKOhvm7NnqhGsLFqjdkQ74iUVR\nFH489SMzt8xE46Xhrbveondkb6vsu1GH9oG0A0zfOF29Gjzkbe5qU2koUnq6OoOZhwd8+SU0s4/q\nMcKxFZWVcaI8wE8UFXG8fDldXExzNzfaVwS5lxex5WEe5enZtG4UUhT44Qe1QrynpzqH95AhDhne\nZcYyPkn8hDnxc7ij9R28Pvh1Wvi3aNB9NsrQTi9M5x8//4P1p9bz8qCXeaLHE7g4V+pH275dnaXv\niSfU/zgO2scmHEeZonBBpzOF+MniYk6Wf80uKaGNp6cpxNt5e9POy4u2Xl6Eu7s33nHmRqN6Z+Xc\nuaDRqN0nI0Y4ZLdJgb6A17e9zr/2/Ytpvacxo++MBrtY2ahCW1eq472d7/HW728xrvs4XhrwEgGe\nAZX3qA7+f/VV+PhjGD7covsXoj60ZWWcrhTip8rPzE8VF6MtK6ONl5cpxNt6edGmfIn08GgcF0PL\nytRCIosWQVGROh3s2LEOeXflubxzzNwykx0Xd7DozkU81OUhi//RbRShrSgK3x//nuc2PUe3sG68\nedebtG3WtuqLCgvVOngnT8Lq1dC6tUX2LURDyi8tNQX46eJikit9vVxaSisPD1OIt/HyIsbTkxgv\nL1p7euLtaJ8gFQV+/VUN76NH1WGCEyeCv+PNgf3b+d+YvnE6Hi4eLBm2hJsjbrbYth0+tE/mnGTq\nT1O5lH+JJUOXMDhm8LUvOn5crY5+223qzGRSSUU0AkVlZZwpLiZZpyO5uJizOh1nios5o9NxTqcj\n0NW1SohHe3rSunyJ9PCw71EuBw7Am2/Cpk3qENxJk6Bt29rfZ0eMipEViSuY9cssRrUfxcI7Flqk\n+LDDhrbWoGXhbwv5cN+HzOo/i6m3TsXN5Q+FSI1GddL2BQvg9dfVM20hmgCjopBmMJhC/Gx5qFcs\nmQYDLTw8iC4P82hPT1pVetzC3d0+Qv3sWVi+HD75BHr0gClT1BEnDjQSJ0+Xx5xf57Dq6CoWDFpw\n7TW2OnK40K4Ywvfspmfp17Ifb971ZvXzApw5o/6FLitTf+AO9ldaiIakNxq5oNNxvvysvGI5r9dz\nrjzUw93daVke5q08PGjl6ak+9/CgpbW7X3Q69aLl8uVw4QJMmKCehDnQlLCJ6Yk89eNT6Mv0LBu+\njFta3FKv7ThUaJ/KOcVTPz1FakEqS4ctZWB0NTfCGI3wr3+po0JmzVJnH3O0vj0hbMxgNHJJr+e8\nTseF8q+mRa/nkl6Pj7MzLT09aVke4i09PIjy9CTKw4MoDw/CG+ps/dAhNbxXrYK+fdWLliNHgo+P\n5fdlYYqi8OmhT5m5ZSYjYkfw2uDX6txl4hChrS/V88b2N1i8a3HNXSEA58+rw/gKC9Wz6w4dLNBM\nIcQfKYpCVkkJF8pD/aJef/WxTsdFvZ6skhJC3d1NIR5VHuqRHh6mJczdvf5j1AsKYM0a+Pxz2LFD\n7TZ5+GF1ali3avLBjlR0mfzv2P948643Gdt1rNmjTOw+tLee38qkdZOIDYpl6bCl1RfP1evVs+tX\nXoEZM9QJahyoz0uIxqjEaCTVYDCF+MXyM/TKS3Z5sEd6eNDC3Z0W5WHeonyJ9PAgwt0dr9o+LWdm\nwtdfwxdfqPOdPPCAWj1+wAD1Bjo7tSdlDxPXTSTIK4jldy83q/iC3YZ2TlEOf9/8dzad2cT7w95n\ndIfR176orEz9Ic2Zc3UO386dLdA0IYQ1lBiNpBkMXNTrSam0XNLrSTEYuKTXk6rX4+PiQovyAK/y\ntfxxhIcHoW5uanfMmTPw1Vfq/N7HjsGdd8Ldd6v3Zdjh3PilxlKW7FrCq7+9yjN9nuH525/H3aXm\nMep2F9qKovDZoc94fvPz/KXzX1hwxwL8Pfz/+CJ1vpBZs8DXVx0Z4oAFRoUQtVMUhZySElIMBlIr\ngt1gIEWvJ63831INBnJKSmju5kaEuzvh5WEeXlpK+IkThO/cSfgvvxAREEDogAG4DhgAvXvb1Xz5\n5/PO89RPT5F8OZkP7vmA/q36V/u6hgztocB7gAvwb2DRH9ZfE9rn884zad0kMrQZfHjPh9VfXd22\nTZ3qMS9PvbNxxAiHnLNACGFZpUYjGSUlpJWHelpFqFc81utJLSwkW1FoptUSlpWlhrq3N2HBwYS3\nbk14YCBh7u6mxdfFxarTCFSMjpu2YRoj249k0Z2L8PPwq/KahgptF+AEcCeQAuwBxgBJVdunhrZR\nMbJ8z3Lmxs/ludueY0bfGVUvNKanX+2vSktTJ5h55JFGMyokPj6euLg4WzfDLsixuEqOxVWWPBal\nRiNZJSWk5+eTduQIaadOkZaaSrpWS1pEBBnh4aQHBpLm4QHOzoSVXzANc3cntFKgVzwOdXMj1Jx+\n9zrI0+Xx3Mbn2HJ2Cx/c8wFD2w41ratvaNd2le9W4DRwrvz5V8AoqoY2oN7R+Ncf/kqpsZTfxv1G\nx+DyunL5+fDdd2pQ796tDumZPx8GD250Fxnll/MqORZXybG4ypLHwtXZmXAPD8KDg+kxaBAMGqSu\nKC2FI0fg4EHYvBkOHqTwxAnSAwNJ79WLtI4dyYiIID04mD3+/qR7epKhKKQbDGQYDHg4OxNaKcRN\nS/nzkPLHIe7u+NVyBh/oGch/Rv2HzcmbmbhuIgNbDeSdP72jFmyp7/ddy/oWwMVKzy8B10w2++b2\nN1m07XVe6/oM4wMH4bIlEc59D/v2qQctLk4dwvfdd3bV9ySEaIRcXaF7d3Up56sotE1Pp+3Bg5CU\npFbgOXv26uLlBa1bo0RGciUigoyICDJCQ8lo1oyMgAAyfHzY7+pKppMTGYpCZmkpGQYDZUBIRZi7\nuRFc/jXkD187tujP3kkHmf/rS3RZ1oWlw5fW/9urZb1ZA7AffHAez+UacfZZDNFr1EmcWrdWx1t+\n+KHMcS2EsC0nJwgPV5ehQ6uuUxR1qOHZszilphKYmUlgVhbtDx6ErCx1XVaW2mtQWKgupaXg64s2\nKIjM0FAymzUjKzCQzIAAMv39SfH354CfHxm+vmR5e5Pp7U22tzdeznfTPHoAc35Pr/+3Usv6PsA8\n1IuRAC8CRqpejDwNtKl3C4QQomlKBiw+L4dr+YajAXcgEeho6Z0IIYSwnGGoI0hOo55pCyGEEEII\nISxpKHAcOAXMrOE1S8rXHwR6WKldtlDbsRiLegwOAduBm6zXNKsz5/8FwC1AKfBnazTKRsw5FnHA\nAeAIEG+VVtlGbceiObABtcv1CPB/VmuZdf0XyAAOX+c1DZKbLqjdI9GAG9X3bQ8Hfix/3BvYaamd\n2xlzjsVtQEVRy6E07WNR8bpfgHXAfdZqnJWZcywCgaNAZPnz5tZqnJWZcyzmAa+VP24O5FD7aDZH\n1B81iGsK7TrnprmT5Fa+yaaEqzfZVDYSWFH+eBfqf9BQM7fvSMw5FjuAK+WPd3H1l7SxMedYAEwF\nvgGyrNYy6zPnWDwMrEa93wEg21qNszJzjkUaUDEZkT9qaJdaqX3W9BuQe531dc5Nc0O7uptsWpjx\nmsYYVuYci8qe4Opf0sbG3P8Xo4Dl5c8tUwXa/phzLNoBzYBfgb3Ao9ZpmtWZcyw+AjoDqajdAtOs\n0zS7U+fcNPfjiLm/aH8c990Yf0Hr8j0NAsYDtzdQW2zNnGPxHvBC+WudsMzMkvbInGPhBvQEBgPe\nqJ/IdqL2ZzYm5hyLWajdJnGo93lsBroBBQ3XLLtVp9w0N7RTgMpVC6K4+hGvptdElv9bY2POsQD1\n4uNHqH3a1/t45MjMORa9UD8eg9p3OQz1I/MPDd466zLnWFxE7RIpLl+2ogZVYwttc45FX2Bh+eNk\n4CzQHvUTSFPSYLlpzk02lTvU+9B4L76Zcyxaovbp9bFqy6yvrjdffUzjHT1izrHoAGxBvVDnjXpx\nqpP1mmg15hyLd4C55Y9DUUO9sc53EY15FyItnpvV3WQzqXypsLR8/UHUj4GNVW3H4t+oF1YOlC+7\nrd1AKzLn/0WFxhzaYN6xmIE6guQw8LRVW2ddtR2L5sBa1Kw4jHqRtjH6ErXf3oD6SWs8TTc3hRBC\nCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhLgx/w+lAzxyK92ZeQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb2df410>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u30d9\u30fc\u30bf\u5206\u5e03\u3082\u81ea\u7136\u306a\u89e3\u91c8\u306f\u96e3\u3057\u304f\u3001\u9006\u30ac\u30f3\u30de\u5206\u5e03\u3068\u540c\u69d8\u306b\u30d9\u30a4\u30ba\u7d71\u8a08\u5b66\u306b\u304a\u3044\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u5178\u578b\u7684\u306a\u5229\u7528\u4f8b\u306f\u3001$\\mathrm{Bern}(p)$ \u3084 $\\mathrm{Bin}(n,p)$ \u306a\u3069\u306e\u78ba\u7387\u30d1\u30e9\u30e1\u30fc\u30bf $p$ \u306e\u63a8\u5b9a\u3067\u3059\u3002\u3053\u306e\u610f\u5473\u306f\u9006\u30ac\u30f3\u30de\u5206\u5e03\u306e\u5834\u5408\u3088\u308a\u5206\u304b\u308a\u3084\u3059\u3044\u306e\u3067\u4ee5\u4e0b\u5177\u4f53\u4f8b\u3092\u4e0a\u3052\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\n",
      "\n",
      "\u4f8b\u3068\u3057\u3066\u3001\u3044\u3073\u3064\u306a\u30b3\u30a4\u30f3\u306e\u8868\u304c\u51fa\u308b\u78ba\u7387 $\\theta$ \u3092\u30d9\u30a4\u30ba\u7684\u306b\u63a8\u5b9a\u3059\u308b\u3068\u3057\u3066\u3001$\\theta$ \u306e\u5024\u306b\u5bfe\u3059\u308b\u4e8b\u524d\u5206\u5e03(\u4e8b\u524d\u306e\u4fe1\u5ff5)\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3066\u307f\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4f8b1: $\\theta=1/2$ \u306b\u975e\u5e38\u306b\u8fd1\u3044\u5024\u3060\u3068\u4fe1\u3058\u3066\u3044\u308b\u4eba\u306e\u4e8b\u524d\u5206\u5e03"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 1)\n",
      "plot(x, stats.beta(100, 100).pdf(x), label='Beta(100,100)')\n",
      "xlabel(r'$\\theta$')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 52,
       "text": [
        "<matplotlib.legend.Legend at 0xb790150>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x99dad50>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4f8b2: $\\theta=1/2$ \u306b\u975e\u5e38\u306b\u8fd1\u3044\u5024\u3060\u3068\u3082\u3063\u3068\u5f37\u304f\u4fe1\u3058\u3066\u3044\u308b\u4eba\u306e\u4e8b\u524d\u5206\u5e03"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 1, 1000)\n",
      "plot(x, stats.beta(10000, 10000).pdf(x), label='Beta(10000,10000)')\n",
      "xlabel(r'$\\theta$')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "<matplotlib.legend.Legend at 0xb90e6d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pNlAkE3TiVVyVbMg3Af8D+BQv3E/g9eArgEZ/nUZ/WiTn6ZuhxFX5SW53OfC3eGWbk8D/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\nYPn/kktzczoHPZQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb404550>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4f8b3: $\\theta=1/2$ \u306e\u8fba\u3060\u308d\u3046\u3068\u601d\u3063\u3066\u3044\u308b\u3051\u3069\u3042\u307e\u308a\u81ea\u4fe1\u304c\u306a\u3044\u4eba\u306e\u4e8b\u524d\u5206\u5e03"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 1)\n",
      "plot(x, stats.beta(2.0, 2.0).pdf(x), label='Beta(2,2)')\n",
      "xlabel(r'$\\theta$')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "<matplotlib.legend.Legend at 0xb961ed0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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79rB9O0yf7nUkBRO3Lfdt22xP1BUroHLliL2siMShd9+F0aO9SfBquefwyitw\n++1K7CJSdB072uSMWbO8jiR4cdly374dzj3XVpdVrRqRlxSRODdiBHzySeQHV9Vyz2bgQPj735XY\nRSR0One24oPz5nkdSXDiruW+axfUqmWryqpXD/vLiUgCGToUvvoqsgub1HL3e+MNuP56JXYRCb0u\nXWDxYuvyjXZx1XLfvx9q1ACfz2bKiIiE2ssvw6JFNv89EsK1QXYohT25v/EGTJ0KX3wR1pcRkQT2\n229wzjnw44/2b7iFs1umNbYJ9hrg8XyOuwTbUPumggYRCocOwYAB0Lu3F68uIomiXDno2tWmW0ez\nQMm9GDAES/D1gA5Abh0exYD+wBQi+2ngqE8+gWrV4LLLvHh1EUkkPXvCRx/B//7ndSR5C5TcLwXW\nAhuBTGAs0DaX4x4EPgN+DWVwwXIO+vdXq11EIuOMM6wsweDBXkeSt0DJvQqQlu1xuv9rOY9pCwz1\nP454Xd8pU+zf1q0j/coikqj+7/9sauTvv3sdSe6KB3g+mET9GtDbf2wS+XTLpKamHr2fkpJCSkpK\nEKcPrH9/eOwxb3dLEZHEUrMmtGoFw4fDww+H7rw+nw+fz1fk8wRKh5cBqVifO0AfIAvrXz9ifbbz\nVAL2A/cCE3KcKyyzZebNgw4dbAu94oHeqkREQmjhQtuxaf16KFkyPK8RrtkyC4DaQHWgJNCeE5P2\nOUAN/+0z4L5cjgmb/v3hkUeU2EUk8i66COrVgw8+8DqSEwVK7oeAB4BvgJXAx8DPQDf/zVM//wxz\n5tiqMRERL/TubY3MrCyvIzleTC9i6tLFVqT+858hPa2ISNCcg0svhSefhBtvDP35E26Fano6XHAB\nrF0LFSuG7LQiIgX2+edWlmDu3NBP7Ei4wmEDB9oWekrsIuK1G2+EnTth5kyvIzkmJlvuu3bZNCRt\nxiEi0WLECBg3DiZPDu15E6rlPnw4XHedEruIRI9OnWxq5MqVXkdiYq7lnplpldgmTIBGjUIQlYhI\niDz7rI0Hvv126M6ZMAOqH35oH3+mTQtBRCIiIfTrr7Z/8y+/wGmnheacCdEt45yV2QzlUl8RkVA5\n7TS49VarOeO1mGq5z5wJ995ri5f+FFNvSyKSKFauhJYtYeNGOPnkop8vIVrur74KvXopsYtI9KpX\nz8oSRGobvrzETMt9zRq4/HJ7N0xODl1QIiKh9t138NBDsGxZ0Rc1xX3LfdAg29pKiV1Eol2rVtbD\nMHWqdzEenwLQAAAIu0lEQVTERMt9505btLRyJVSuHOKoRETCYPRo24rvm2+Kdp64brkPGwZt2yqx\ni0js6NABli6F5cu9ef2ob7kfPGiVHydPhoYNwxCViEiYPP88bNgAI0cW/hxxu4hpzBh4910boBAR\niSXbt0Pt2rBqlW2qXRhx2S3jnE1/1KIlEYlFlSpB+/bw5puRf+2obrlPnw733w8rVmhuu4jEplWr\n4MorbRp3qVIF//64bLlr0ZKIxLq6deGSS+D99yP7usGmzdbAKmAN8Hguz98OLAGWArOBC4oa2Nq1\nMG+eldEUEYllDz1ka3VCvNNovoJJ7sWAIViCrwd0AM7Lccx6oDmW1J8Dilzw8o034J57tGhJRGJf\nq1a2gbbPF7nXDCa5XwqsBTYCmcBYoG2OY+YCe/z35wNnFSWovXvhvffgvvuKchYRkeiQlAQPPgiD\nB0fuNYNJ7lWAtGyP0/1fy8s9QJE2mhozxgYgzj67KGcREYked9wBM2bAf/4TmdcLJrkXpJeoBdCF\n3Pvlg+IcDBli73IiIvGiTBno3Dlytd6LB3HMZiD7bqVVsdZ7ThcAw7G++V25nSg1NfXo/ZSUFFJS\nUk44Zto0mx2Ty1MiIjGtRw9o2hT69s17WqTP58MXgs75YOZOFgdWA62ALcCP2KDqz9mOqQZMAzoB\n8/I4T1Dz3G+8Edq0gW7dgohMRCTGXHst3HwzdOkS3PHhLj/QBngNmzkzEngROJJ+hwEjgHbAJv/X\nMrGB2OwCJveNG6FxY+uTKl06yMhERGLIlCnQpw8sXBhcrfe4qC3z2GNw+LDtkyoiEo+ysmxh0zvv\nwBVXBD4+5pP7/v1QrRr8+COcc04EoxIRibDBg2HWLPjkk8DHxnz5gQ8+sIEGJXYRiXd33mmVbtNz\nm5oSIlGR3J2zdzJNfxSRRFCuHNx+O7z1VvheIyqS+8yZkJkJV13ldSQiIpHxwAMwfDgcOBCe80dF\nch882H7Qou4SLiISK+rUgQsvDK7fvTA8H1BNS7MfcONGKFs2gtGIiHjsq6/gmWdsIklejduYHVAd\nOtTK+iqxi0iiadMGdu6E+fNDf25PW+4ZGTb9cdYsOPfcCEYiIhIlXnkFliyxSri5KWzLPZjaMmEz\nbhw0aKDELiKJ6667oFYt2LEDTj01dOf1tFvmrbdUs11EEtupp8INN8Do0aE9r2fdMitWwF//anVk\nSpSIYBQiIlFm7lwrB7x69Yl7RsfcgOqwYbaNnhK7iCS6yy6zYonTpoXunJ603Pfts4HURYvsXxGR\nRPfWWzB1Knz++fFfj6mW+9ixcPnlSuwiIkfcfjtMnw5btoTmfJ4k96FDNZAqIpJd2bLQvj2MGBGa\n80W8W2bBArj1Vli7FooVi+Cri4hEuSVL4LrrYMMGKO6fqB4z3TJDh9oWekrsIiLHa9gQqlaFSZOK\nfq6Ittx37XLUqGHTfU4/PYKvLCISI8aMgQ8/hK+/tscx0XJ/7z1o3VqJXUQkL7feCgsWwPr1RTtP\nMMm9NbAKWAM8nscxr/ufXwI0yutEb70F3bsXNEQRkcRx8sm2U9OwYUU7T6DkXgwYgiX4ekAH4Lwc\nx1wD1AJqA12BofmdsHnzQsUZV3w+n9chRA1di2N0LY5J9GvRrRuMGmXFFQsrUHK/FFgLbAQygbFA\n2xzH3AC8678/HygPnJHbybp314YcoF/c7HQtjtG1OCbRr0Xt2ja4mnNBU0EESu5VgLRsj9P9Xwt0\nzFm5naxz54KGJyKSmLp3L9oeq4GS+4lbJ+UuZ3s81+8rXz7Is4mIJLgbboB16wr//YE6SS4DUrE+\nd4A+QBbQP9sxbwE+rMsGbPD1SmBbjnOtBWoWPlQRkYS0DhvXDKni/hNXB0oCi8l9QHWy//5lwLxQ\nByEiIqHXBliNtbz7+L/WzX87Yoj/+SXARRGNTkRERERECidki57iQKBrcTt2DZYCs4ELIhdaxAXz\newFwCXAIuCkSQXkgmOuQAiwClmPjWfEq0LWoBEzBuoOXA3dFLLLIewcbp1yWzzGe5s1iWPdMdaAE\ngfvomxC/ffTBXIu/AKf477cmsa/FkeOmAV8BN0cquAgK5jqUB1ZwbDpxpUgFF2HBXItU4EX//UrA\nDmwcMB41wxJ2Xsm9wHkz1LVlQrroKcYFcy3mAnv89+eTx/qAOBDMtQB4EPgM+DVikUVWMNehI/A5\ntl4EYHukgouwYK7FVqCc/345LLkfilB8kTYL2JXP8wXOm6FO7iFd9BTjgrkW2d3DsXfmeBPs70Vb\njpWvCHaNRSwJ5jrUBioC04EFwB2RCS3igrkWw4HzgS1YV0TPyIQWlQqcN0P9ESeki55iXEF+phZA\nF+DyMMXitWCuxWtAb/+xSUS2HHWkBHMdSmAzzloBydinu3lYX2s8CeZaPIF116Rga2SmAg2B38MX\nVlQrUN4MdXLfDFTN9rgqxz5e5nXMWf6vxZtgrgXYIOpwrM89v49lsSyYa3ExxxbCVcKm4GYCE8Ie\nXeQEcx3SsK6YP/y3mVhCi7fkHsy1aAr0899fB2wA6mCfaBKN53lTi56OCeZaVMP6HS+LaGSRF8y1\nyG4U8TlbJpjrUBf4DhtwTMYG2OpFLsSICeZavAr09d8/A0v+FSMUnxeqE9yAqmd5U4uejgl0LUZg\ng0SL/LcfIx1gBAXze3FEvCZ3CO46/B82Y2YZ8P8iGl1kBboWlYCJWJ5Yhg02x6uPsLGFg9inty4k\nbt4UERERERERERERERERERERERERERERERERkVhQzOsARDyWhK0CvAgrvxyv9X1ERBLKQ8CF2O7y\n+e0QJRJTQl3PXSSWlACuw4pWnc2xXbFEYp6SuySyllht8DuB+zh+MwSRmKbkLonsL8BIbPuyk7GN\nMUTigpK7JLLKwHrgJP/9xd6GIxI6Su6SyHYAGVjt+Fc9jkUkpDQVUhLZ/4DrsUbOOx7HIiIiIiIi\nIiIiIiIiIiIiIiIiIiIiIiIiIiIiEjv+PwZD/GQQvvV4AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb90e590>"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\u4f8b4: \u7d76\u5bfe\u8868\u304c\u51fa\u308b\u30a4\u30ab\u30b5\u30de\u30b3\u30a4\u30f3\u3060\u3068\u4fe1\u3058\u3066\u3044\u308b\u4eba\u306e\u4e8b\u524d\u5206\u5e03"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 1)\n",
      "plot(x, stats.beta(2.0, 0.1).pdf(x), label='Beta(2,0.1)')\n",
      "xlabel(r'$\\theta$')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "<matplotlib.legend.Legend at 0xbbffb10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YORfnAO9hLjgOxFxkG+deiK6xcy7+C3gwVC/AJP98l+JzWxH2Lqh6ljd101Or\n7s7FEswFos2h8pHbAbrIzt+LMD8nd7B3Ln6NmTHzCfALV6NzV3fnYijwFiZXfIK52OxHf8FcVziJ\n+Z/bAlI3b4qIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIhIMkj3OgARj6Vh7gKcill+2a/r+4iIpJRf\nApMxT5fv6glRIknF6fXcRZJJP+AKzIJVZ9D6VCyRpKfkLqnse5h1wf8VuJW2D0MQSWpK7pLKLgSe\nxjy+bADmoRgivqDkLqlsGPAZkBGqb/E2HBHnKLlLKqsEGjBrx/+Xx7GIOEpTISWVfQ38L0wn5xmP\nYxEREREREREREREREREREREREREREREREREREUke/x/EWQb2Yq2ISwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb7afb10>"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## \u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\n",
      "$K$ \u6b21\u5143\u306e\u30d1\u30e9\u30e1\u30fc\u30bf $\\boldsymbol{\\alpha}=(\\alpha_1,\\alpha_2,\\ldots,\\alpha_K)\\quad(\\alpha_i >0)$ \u306b\u5bfe\u3057\u3066\uff0c$K$ \u6b21\u5143\u78ba\u7387\u5909\u6570 $\\mathbf{X}$ \u4e0a\u306e\u5bc6\u5ea6\u95a2\u6570\u304c\n",
      "\n",
      "$$ \\pi(\\mathbf{x}) \\propto \\prod_{i=1}^{K}x_i^{\\alpha_i-1} \\qquad (x_1,x_2,\\ldots,x_K\\geq 0, x_1+x_2+\\cdots+x_K=1) $$\n",
      "\n",
      "\u3068\u8868\u3055\u308c\u308b\u78ba\u7387\u5206\u5e03\u3092**\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03(Dirichlet distribution)**\u3068\u547c\u3073$\\mathrm{Dirichlet}_K(\\mathbf{X}|\\boldsymbol{\\alpha})$\u3068\u66f8\u304d\u307e\u3059\u3002\n",
      "\u5e73\u5747\u306f$\\mathrm{E}[\\mathbf{X}] = \\frac{1}{\\sum_{i=1}^K\\alpha_i}\\boldsymbol{\\alpha}$\u3067\u3001\u5206\u6563\u5171\u5206\u6563\u884c\u5217\u306f\n",
      "\n",
      "$$\\Sigma_{ii} = \\frac{\\alpha_i(c-\\alpha_i)}{c^2(c+1)},\\quad\\Sigma_{ij} = \\frac{-\\alpha_i\\alpha_j}{c^2(c+1)}\\qquad(c = \\sum_{i=1}^K\\alpha_i)$$\n",
      "\n",
      "\u3067\u3059\u3002\n",
      "\n",
      "\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\u306f\u30d9\u30fc\u30bf\u5206\u5e03\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3067\u3001$\\mathrm{Beta}(X|\\alpha,\\beta) = \\mathrm{Dirichlet}_K((X, 1-X) | (\\alpha,\\beta))$ \u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\n",
      "\u4f7f\u3044\u65b9\u3082\u30d9\u30fc\u30bf\u5206\u5e03\u3068\u540c\u69d8\u3067\u3001$\\mathrm{Cat}_K(\\mathbf{p})$ \u3084 $\\mathrm{MultiNomial}_K(n,\\mathbf{p})$ \u306a\u3069\u306e\u78ba\u7387\u30d1\u30e9\u30e1\u30fc\u30bf $\\mathbf{p}$ \u3092\u63a8\u5b9a\u3059\u308b\u969b\u306e\u4e8b\u524d\u5206\u5e03\u3068\u3057\u3066\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u7279\u306b\u81ea\u7136\u8a00\u8a9e\u51e6\u7406\u306a\u3069\u3067\u306f\u6587\u5b57\u3084\u5358\u8a9e\u306e\u51fa\u73fe\u983b\u5ea6(\u30ab\u30c6\u30b4\u30ea\u5206\u5e03\u306b\u5f93\u3046)\u3092\u63a8\u5b9a\u3059\u308b\u554f\u984c\u304c\u983b\u7e41\u306b\u767b\u5834\u3059\u308b\u70ba\u3001\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\u306f\u91cd\u8981\u3067\u3059\u3002\n",
      "\n",
      "\u3084\u306f\u308ascipy.stats\u306b\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\u306f\u7528\u610f\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u304c\u3001numpy.random.dirichlet\u3067\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306f\u51fa\u6765\u307e\u3059\u3002"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### \u4f8b\n",
      "\u4f8b\u3048\u3070\u888b\u306e\u4e2d\u306b\u5927\u91cf\u306e\u8d64\u7403\u3001\u9752\u7403\u3001\u767d\u7403\u304c\u5165\u3063\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3042\u308b\u4eba\u306f\u3001\u3053\u306e\u888b\u306e\u4e2d\u306b\u305d\u308c\u305e\u308c\u304c$\\text{\u8d64}:\\text{\u9752}:\\text{\u767d} = 1:3:2$ \u304f\u3089\u3044\u306e\u6bd4\u7387\u3067\u3067\u5165\u3063\u3066\u3044\u308b\u3060\u308d\u3046\u3068\u601d\u3063\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\u3067\u8868\u3059\u70ba\u306b\u306f $\\boldsymbol{\\alpha}=k(1,3,2)\\quad\\text{($k$\u306f\u5b9a\u6570)}$ \u306e\u30c7\u30a3\u30ea\u30af\u30ec\u5206\u5e03\u3092\u4f7f\u3044\u307e\u3059\u3002$k$ \u306e\u5024\u304c\u5927\u304d\u3044\u307b\u3069\u3001\u3053\u306e\u4eba\u306f\u81ea\u5206\u306e\u4e88\u60f3\u304c\u3088\u308a\u6b63\u78ba\u3060\u3068\u601d\u3063\u3066\u3044\u308b\u4e8b\u306b\u306a\u308a\u307e\u3059\u3002\u6563\u5e03\u56f3\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u9055\u3044\u3092\u307f\u3066\u307f\u307e\u3057\u3087\u3046\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "fig = figure()\n",
      "ax = Axes3D(fig)\n",
      "ax.set_xlim(0,1)\n",
      "ax.set_ylim(0,1)\n",
      "ax.set_zlim(0,1)\n",
      "ax.set_xlabel('red')\n",
      "ax.set_ylabel('blue')\n",
      "ax.set_zlabel('white')\n",
      "ax.view_init(azim=30)\n",
      "\n",
      "N = 300\n",
      "\n",
      "# Dirichlet_3(X | (1, 3, 2)) \u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u4f8b\n",
      "samples = array( random.dirichlet([1, 3, 2], N) )\n",
      "ax.scatter(samples[:,0], samples[:,1], samples[:,2], color='blue', label='Dirichlet3(1,3,2)')\n",
      "print average(samples, axis=0)\n",
      "\n",
      "# Dirichlet_3(X | 10(1, 3, 2)) \u304b\u3089\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u4f8b\n",
      "samples = array( random.dirichlet([10, 30, 20], N) )\n",
      "ax.scatter(samples[:,0], samples[:,1], samples[:,2], color='red', label='Dirichlet3(10,30,20)')\n",
      "print average(samples, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.18127278  0.50421982  0.31450741]\n",
        "[ 0.17153889  0.49183437  0.33662673]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bxHVEm5UrYzQ3awQCasJ3u+GEE4b3YtTUBLfcovH5zxvcfrsWdzcORE0NrFhh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gqh7YDniRG1vD6DAUYSV0JrAfDww1w9oye9Fnv6JMvKgNdfV6G6Wsjz/fabApWVFObNY9CihfC6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\nMjKNgv8HnmTynNmBg8IAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb91f710>"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## $\\chi^2$ \u5206\u5e03\n",
      "\n",
      "$Z_1,\\ldots,Z_K\\stackrel{\\text{i.i.d.}}{\\sim}\\mathrm{N}(0,1)$ \u306e\u6642\uff0c\n",
      "$$ X=Z_1^2 + \\cdots + Z_K^2 $$\n",
      "\u306e\u5f93\u3046\u78ba\u7387\u5206\u5e03\u3092\u81ea\u7531\u5ea6 $K$ \u306e**$\\chi^2$(\u30ab\u30a4\u4e8c\u4e57)\u5206\u5e03(chi squared distribution)**\u3068\u547c\u3073\uff0c$\\chi^2_K(X)$ \u3068\u66f8\u304d\u307e\u3059\u3002$\\chi^2$\u691c\u5b9a\u306a\u3069\u3001\u7d71\u8a08\u5b66\u3067\u975e\u5e38\u306b\u826f\u304f\u4f7f\u3046\u3053\u3068\u306b\u306a\u308b\u5206\u5e03\u3067\u3059\u3002\u5bc6\u5ea6\u95a2\u6570\u306f\n",
      "\n",
      "$$ \\pi(x) \\propto x^{K/2-1}e^{-x/2}$$\n",
      "\n",
      "\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u304b\u3089 $\\chi^2$ \u5206\u5e03\u306f\u30ac\u30f3\u30de\u5206\u5e03\u306e\u4e00\u7a2e\u3067\u3042\u308a\n",
      "\n",
      "$$ \\chi^2_K(X) = \\mathrm{Gamma}(X|K/2, 1/2) $$\n",
      "\n",
      "\u3067\u3042\u308b\u4e8b\u304c\u5224\u308a\u307e\u3059\u3002\u307e\u305f\n",
      "\n",
      "$$ \\mathrm{E}[X] = K,\\qquad\\mathrm{V}[X]=2K$$\n",
      "\n",
      "\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 10)\n",
      "plot(x, stats.chi2(1).pdf(x), label=u'$\\chi^2_1$')\n",
      "plot(x, stats.chi2(2).pdf(x), label=u'$\\chi^2_2$')\n",
      "plot(x, stats.chi2(3).pdf(x), label=u'$\\chi^2_3$')\n",
      "plot(x, stats.chi2(4).pdf(x), label=u'$\\chi^2_4$')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "<matplotlib.legend.Legend at 0xc26f650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cEKBunu7cqb6pfPut+rYydy5cuOC4SgkhmjR7o/944P9QI2E+Bl4Hpln3LQA+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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb978b50>"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## $t$\u5206\u5e03\n",
      "\n",
      "\u5b9a\u6570 $\\nu \\geq 1$ \u306b\u5bfe\u3057\u3066 $X > 0$ \u4e0a\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u304c\n",
      "\n",
      "$$\\pi(x) \\propto \\left(1+\\frac{x^2}{\\nu}\\right)^{-(\\nu+1)/2}$$\n",
      "\n",
      "\u3068\u8868\u3055\u308c\u308b\u5206\u5e03\u3092\u81ea\u7531\u5ea6 $\\nu$ \u306e**$t$\u5206\u5e03(t distribution)** \u307e\u305f\u306f\u30b9\u30c1\u30e5\u30fc\u30c7\u30f3\u30c8\u306e $t$ \u5206\u5e03\u3068\u547c\u3073\u3001$t_{\\nu}(X)$ \u3068\u66f8\u304d\u307e\u3059\u3002\u3053\u306e\u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570\u304c\u4f55\u3092\u8868\u3059\u306e\u304b\u3068\u3044\u3046\u4e8b\u306f\u7d71\u8a08\u5b66\u306b\u5165\u3063\u3066\u304b\u3089\u8aac\u660e\u3057\u307e\u3059\u304c\u3001\u7d71\u8a08\u5b66\u306b\u304a\u3044\u3066\u6975\u3081\u3066\u91cd\u8981\u306a\u5206\u5e03\u3067\u3059\u3002$t$ \u5206\u5e03\u306f $\\nu\\rightarrow\\infty$ \u306e\u6642\u6a19\u6e96\u6b63\u898f\u5206\u5e03 $\\mathrm{N}(0,1)$ \u3068\u4e00\u81f4\u3057\u307e\u3059\u3002$t$ \u5206\u5e03\u306e\u5e73\u5747\u5024\u3001\u5206\u6563\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\n",
      "\n",
      "$$ \\mathrm{E}[X] = 0\\quad (\\nu > 1\\text{\u306e\u6642}),\\qquad \\mathrm{V}[X] = \\frac{\\nu}{\\nu-2}\\quad(\\nu > 2\\text{\u306e\u6642})$$\n",
      "\n",
      "\u30ab\u30c3\u30b3\u5185\u306e\u6761\u4ef6\u304c\u6e80\u305f\u3055\u308c\u306a\u3044\u6642\u3001\u5e73\u5747\u3084\u5206\u6563\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(-3, 3)\n",
      "plot(x, stats.t(1).pdf(x), label='$t_1$')\n",
      "plot(x, stats.t(2).pdf(x), label='$t_2$')\n",
      "plot(x, stats.t(3).pdf(x), label='$t_3$')\n",
      "plot(x, stats.t(4).pdf(x), label='$t_4$')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "<matplotlib.legend.Legend at 0xc3274d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xghIlSrBhwwajvKY+RSzaAUsAU+B34PWipz2RG2+bAM+AQcD1xHO+wFMgAYgD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\nQgjxO/4D/Ag+KemrVyUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa3fc9d0>"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## $F$\u5206\u5e03\n",
      "\n",
      "$X_1\\sim\\chi^2_{\\nu_1}, X_2\\sim\\chi^2_{\\nu_2}$\u3067 $X_1,X_2$ \u304c\u72ec\u7acb\u306e\u6642\u306b\n",
      "\n",
      "$$ X = \\frac{X_1}{X_2} $$\n",
      "\n",
      "\u306e\u5f93\u3046\u5206\u5e03\u3092 \u81ea\u7531\u5ea6 $\\nu_1,\\nu_2$ \u306e**$F$ \u5206\u5e03(F distribution)**\u3068\u547c\u3073 $F(X|\\nu_1,\\nu_2)$ \u3068\u66f8\u304d\u307e\u3059\u3002\n",
      "\n",
      "$$ \\pi(x)\\propto \\frac{1}{x}\\left(\\frac{\\nu_1x}{\\nu_1x+\\nu_2}\\right)^{\\nu_1/2}\\left(1-\\frac{\\nu_1x}{\\nu_1x+\\nu_2}\\right)^{\\nu_2/2}\\qquad(x\\geq 0)$$\n",
      "\n",
      "$$\\mathrm{E}[X] = \\frac{\\nu_2}{\\nu_2-2}\\quad(\\nu_2 > 2),\\qquad\\mathrm{V}[X]=\\frac{2\\nu_2^2(\\nu_1+\\nu_2-2)}{\\nu_1(\\nu_2-2)^2(\\nu_2-4)}\\quad(\\nu_2 > 4)$$\n",
      "\n",
      "$F$ \u5206\u5e03\u3082\u6761\u4ef6\u306b\u3088\u3063\u3066\u306f\u5e73\u5747\u3084\u5206\u6563\u304c\u5b58\u5728\u3057\u306a\u3044\u5206\u5e03\u306e\u4f8b\u3067\u3059\u3002"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0, 3)\n",
      "plot(x, stats.f(1, 1).pdf(x), label='F(1,1)')\n",
      "plot(x, stats.f(2, 1).pdf(x), label='F(2,1)')\n",
      "plot(x, stats.f(3, 3).pdf(x), label='F(3,3)')\n",
      "legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "<matplotlib.legend.Legend at 0xc577310>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xb976290>"
       ]
      }
     ],
     "prompt_number": 59
    }
   ],
   "metadata": {}
  }
 ]
}