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pybokeh/RandomVariateExample

Last active December 21, 2015 13:39
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RandomVariateExample
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RandomVariateExample
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
" I will show 2 ways to generate random numbers. There are so many different distributions, so I will only show Normal/Gaussian distribution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<strong>One way: Using Python's built-in random class(less efficient)</strong>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import random"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Let's see what methods are available in the random class using Python's dir() method:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dir(random)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 27,
"text": [
"['BPF',\n",
" 'LOG4',\n",
" 'NV_MAGICCONST',\n",
" 'RECIP_BPF',\n",
" 'Random',\n",
" 'SG_MAGICCONST',\n",
" 'SystemRandom',\n",
" 'TWOPI',\n",
" '_BuiltinMethodType',\n",
" '_MethodType',\n",
" '_Sequence',\n",
" '_Set',\n",
" '__all__',\n",
" '__builtins__',\n",
" '__cached__',\n",
" '__doc__',\n",
" '__file__',\n",
" '__initializing__',\n",
" '__loader__',\n",
" '__name__',\n",
" '__package__',\n",
" '_acos',\n",
" '_ceil',\n",
" '_cos',\n",
" '_e',\n",
" '_exp',\n",
" '_inst',\n",
" '_log',\n",
" '_pi',\n",
" '_random',\n",
" '_sha512',\n",
" '_sin',\n",
" '_sqrt',\n",
" '_test',\n",
" '_test_generator',\n",
" '_urandom',\n",
" '_warn',\n",
" 'betavariate',\n",
" 'choice',\n",
" 'expovariate',\n",
" 'gammavariate',\n",
" 'gauss',\n",
" 'getrandbits',\n",
" 'getstate',\n",
" 'lognormvariate',\n",
" 'normalvariate',\n",
" 'paretovariate',\n",
" 'randint',\n",
" 'random',\n",
" 'randrange',\n",
" 'sample',\n",
" 'seed',\n",
" 'setstate',\n",
" 'shuffle',\n",
" 'triangular',\n",
" 'uniform',\n",
" 'vonmisesvariate',\n",
" 'weibullvariate']"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Looks like there is a normalvariate and gauss method avialable. We will use Python's built-in help documentation to find out what each one does."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"help(random.normalvariate)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Help on method normalvariate in module random:\n",
"\n",
"normalvariate(self, mu, sigma) method of random.Random instance\n",
" Normal distribution.\n",
" \n",
" mu is the mean, and sigma is the standard deviation.\n",
"\n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"help(random.gauss)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Help on method gauss in module random:\n",
"\n",
"gauss(self, mu, sigma) method of random.Random instance\n",
" Gaussian distribution.\n",
" \n",
" mu is the mean, and sigma is the standard deviation. This is\n",
" slightly faster than the normalvariate() function.\n",
" \n",
" Not thread-safe without a lock around calls.\n",
"\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"So looks like we'll use the gauss() method since it says it is faster than the other method."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mu, sigma = 0, 1\n",
"data = []\n",
"for i in range(0,1000):\n",
" data.append(random.gauss(mu, sigma))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 25
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Plot the histogram of the raw data that we suspect follows a Normal distribution\n",
"count, bins, patches = hist(data,bins=30,normed=True)\n",
"# Plot the theoretical probability distribution function of the Normal distribution\n",
"plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ), linewidth=2, color='r')\n",
"title(\"Histogram\")\n",
"xlabel(\"bin\")\n",
"ylabel(\"Frequency\")\n",
"grid(True)\n",
"show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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HKodqVA7HjkHp0TmHD0Pz5m7kFIHCrX2ncmHw4MEqLy/PVTFDuBHfJ2RlZRkd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\n",
"text": [
"<matplotlib.figure.Figure at 0x4258ab0>"
]
}
],
"prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<strong>Using numpy's random class (more efficient)</strong>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy import random as nprandom"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dir(nprandom)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 36,
"text": [
"['RandomState',\n",
" 'Tester',\n",
" 'WarningManager',\n",
" '__RandomState_ctor',\n",
" '__all__',\n",
" '__builtins__',\n",
" '__cached__',\n",
" '__doc__',\n",
" '__file__',\n",
" '__initializing__',\n",
" '__loader__',\n",
" '__name__',\n",
" '__package__',\n",
" '__path__',\n",
" 'bench',\n",
" 'beta',\n",
" 'binomial',\n",
" 'bytes',\n",
" 'chisquare',\n",
" 'choice',\n",
" 'dirichlet',\n",
" 'exponential',\n",
" 'f',\n",
" 'gamma',\n",
" 'geometric',\n",
" 'get_state',\n",
" 'gumbel',\n",
" 'hypergeometric',\n",
" 'info',\n",
" 'laplace',\n",
" 'logistic',\n",
" 'lognormal',\n",
" 'logseries',\n",
" 'mtrand',\n",
" 'multinomial',\n",
" 'multivariate_normal',\n",
" 'negative_binomial',\n",
" 'noncentral_chisquare',\n",
" 'noncentral_f',\n",
" 'normal',\n",
" 'np',\n",
" 'operator',\n",
" 'pareto',\n",
" 'permutation',\n",
" 'poisson',\n",
" 'power',\n",
" 'rand',\n",
" 'randint',\n",
" 'randn',\n",
" 'random',\n",
" 'random_integers',\n",
" 'random_sample',\n",
" 'ranf',\n",
" 'rayleigh',\n",
" 'sample',\n",
" 'seed',\n",
" 'set_state',\n",
" 'shuffle',\n",
" 'standard_cauchy',\n",
" 'standard_exponential',\n",
" 'standard_gamma',\n",
" 'standard_normal',\n",
" 'standard_t',\n",
" 'test',\n",
" 'triangular',\n",
" 'uniform',\n",
" 'vonmises',\n",
" 'wald',\n",
" 'warn_ctx',\n",
" 'warnings',\n",
" 'weibull',\n",
" 'zipf']"
]
}
],
"prompt_number": 36
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Looking above, looks like maybe the normal() method is what we need"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"help(nprandom.normal)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Help on built-in function normal:\n",
"\n",
"normal(...)\n",
" normal(loc=0.0, scale=1.0, size=None)\n",
" \n",
" Draw random samples from a normal (Gaussian) distribution.\n",
" \n",
" The probability density function of the normal distribution, first\n",
" derived by De Moivre and 200 years later by both Gauss and Laplace\n",
" independently [2]_, is often called the bell curve because of\n",
" its characteristic shape (see the example below).\n",
" \n",
" The normal distributions occurs often in nature. For example, it\n",
" describes the commonly occurring distribution of samples influenced\n",
" by a large number of tiny, random disturbances, each with its own\n",
" unique distribution [2]_.\n",
" \n",
" Parameters\n",
" ----------\n",
" loc : float\n",
" Mean (\"centre\") of the distribution.\n",
" scale : float\n",
" Standard deviation (spread or \"width\") of the distribution.\n",
" size : tuple of ints\n",
" Output shape. If the given shape is, e.g., ``(m, n, k)``, then\n",
" ``m * n * k`` samples are drawn.\n",
" \n",
" See Also\n",
" --------\n",
" scipy.stats.distributions.norm : probability density function,\n",
" distribution or cumulative density function, etc.\n",
" \n",
" Notes\n",
" -----\n",
" The probability density for the Gaussian distribution is\n",
" \n",
" .. math:: p(x) = \\frac{1}{\\sqrt{ 2 \\pi \\sigma^2 }}\n",
" e^{ - \\frac{ (x - \\mu)^2 } {2 \\sigma^2} },\n",
" \n",
" where :math:`\\mu` is the mean and :math:`\\sigma` the standard deviation.\n",
" The square of the standard deviation, :math:`\\sigma^2`, is called the\n",
" variance.\n",
" \n",
" The function has its peak at the mean, and its \"spread\" increases with\n",
" the standard deviation (the function reaches 0.607 times its maximum at\n",
" :math:`x + \\sigma` and :math:`x - \\sigma` [2]_). This implies that\n",
" `numpy.random.normal` is more likely to return samples lying close to the\n",
" mean, rather than those far away.\n",
" \n",
" References\n",
" ----------\n",
" .. [1] Wikipedia, \"Normal distribution\",\n",
" http://en.wikipedia.org/wiki/Normal_distribution\n",
" .. [2] P. R. Peebles Jr., \"Central Limit Theorem\" in \"Probability, Random\n",
" Variables and Random Signal Principles\", 4th ed., 2001,\n",
" pp. 51, 51, 125.\n",
" \n",
" Examples\n",
" --------\n",
" Draw samples from the distribution:\n",
" \n",
" >>> mu, sigma = 0, 0.1 # mean and standard deviation\n",
" >>> s = np.random.normal(mu, sigma, 1000)\n",
" \n",
" Verify the mean and the variance:\n",
" \n",
" >>> abs(mu - np.mean(s)) < 0.01\n",
" True\n",
" \n",
" >>> abs(sigma - np.std(s, ddof=1)) < 0.01\n",
" True\n",
" \n",
" Display the histogram of the samples, along with\n",
" the probability density function:\n",
" \n",
" >>> import matplotlib.pyplot as plt\n",
" >>> count, bins, ignored = plt.hist(s, 30, normed=True)\n",
" >>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *\n",
" ... np.exp( - (bins - mu)**2 / (2 * sigma**2) ),\n",
" ... linewidth=2, color='r')\n",
" >>> plt.show()\n",
"\n"
]
}
],
"prompt_number": 38
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mu, sigma = 0, 1\n",
"variates = nprandom.normal(mu,sigma,1000)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Plot the histogram of the data which we suspect follows a Normal distribution\n",
"count, bins, ignored = plt.hist(variates, 30, normed=True)\n",
"# Plot the theoretical probability distribution function of the Normal distribution\n",
"plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ), linewidth=2, color='r')\n",
"title(\"Histogram\")\n",
"xlabel(\"bins\")\n",
"ylabel(\"Frequency\")\n",
"grid(True)\n",
"show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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nw8SJcMstsGaNk/LC17jkOoeIiAjS0tIq1UxUbM2aNUyePBmr1cq4ceN4+umn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\nWATcWjTtU+CvwDHAF3cE1XUHaJwyRsp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"text": [
"<matplotlib.figure.Figure at 0x3fbe1b0>"
]
}
],
"prompt_number": 32
}
],
"metadata": {}
}
]
}
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