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Sampling Distributions of Sample Proportion
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Sampling Distribution of Sample Proportions\n", | |
| "\n", | |
| "## 1. Gumballs\n", | |
| "\n", | |
| "### 1.1 Theoretical Inference\n", | |
| "\n", | |
| "**Bernoulli:**\n", | |
| "\n", | |
| "Let Y be the random variable of picking up a gumball out of say 10000 balls. 60% of those balls are yellow. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "scrolled": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x24ff13528d0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "%matplotlib inline\n", | |
| "from SDSP import create_bernoulli_population, get_frequency_df, get_density_df\n", | |
| "from random import shuffle, choices\n", | |
| "from bi_to_nor_demo import get_metrics, bare_minimal_plot\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "\n", | |
| "\n", | |
| "N = 10000 # 10000 balls\n", | |
| "p = 0.6 # probability of yellow ball is 0.6, and others (1-0.6)=>0.4\n", | |
| "n_pickups = 10 # sample size\n", | |
| "n_experiments = 2000 # I dont know what this is called \n", | |
| "\n", | |
| "\n", | |
| "# THEORETICAL PDF\n", | |
| "# generate population and calculate theoretical bernoulli pdf\n", | |
| "population = create_bernoulli_population(N,p)\n", | |
| "theor_df = get_frequency_df(population)\n", | |
| "\n", | |
| "\n", | |
| "# STATISTICAL PDF\n", | |
| "# choose sample, take mean and add to X_mean_list. Do this for n_experiments times. \n", | |
| "X_hat = []\n", | |
| "X_mean_list = []\n", | |
| "for each_experiment in range(n_experiments):\n", | |
| " X_hat = choices(population, k=n_pickups) # choose, say 10 samples from population (with replacement)\n", | |
| " X_mean = sum(X_hat)/len(X_hat)\n", | |
| " X_mean_list.append(X_mean)\n", | |
| "stats_df = get_density_df(X_mean_list, n_pickups)\n", | |
| "\n", | |
| "\n", | |
| "# plot both theoretical and statistical outcomes\n", | |
| "fig, (ax1,ax2) = plt.subplots(2,1, figsize=(5,10))\n", | |
| "from SDSP import plot_pdf\n", | |
| "mu,var,sigma = get_metrics(theor_df)\n", | |
| "plot_pdf(theor_df, ax1, n_pickups, mu, sigma, p, title='True Population Parameters',norm_off=True)\n", | |
| "\n", | |
| "mu,var,sigma = get_metrics(stats_df)\n", | |
| "DD = stats_df['d(x)'].tolist() # we draw density discrete function not probability discrete\n", | |
| "plot_pdf(stats_df, ax2, n_pickups, mu, sigma, p=mu,\n", | |
| " title='Sampling Distribution of\\n a Sample Proportion', dd=DD)\n", | |
| "plt.tight_layout()\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x24ff2d49cf8>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = plt.subplots(1,1, figsize=(5,5))\n", | |
| "\n", | |
| "ax.hist(X_mean_list,100)\n", | |
| "\n", | |
| "plt.show()" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python [conda env:Anaconda3]", | |
| "language": "python", | |
| "name": "conda-env-Anaconda3-py" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.6.4" | |
| }, | |
| "toc": { | |
| "base_numbering": 1, | |
| "nav_menu": { | |
| "height": "225px", | |
| "width": "290px" | |
| }, | |
| "number_sections": true, | |
| "sideBar": true, | |
| "skip_h1_title": false, | |
| "title_cell": "Table of Contents", | |
| "title_sidebar": "Contents", | |
| "toc_cell": false, | |
| "toc_position": { | |
| "height": "calc(100% - 180px)", | |
| "left": "10px", | |
| "top": "150px", | |
| "width": "330px" | |
| }, | |
| "toc_section_display": true, | |
| "toc_window_display": true | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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When
, the discrete probability distribution may not align with continuous normal approximation because pdf can exceed 1 (only the total area is and should be 1). but our discrete probability distribution will not So sometimes we want to use density function to show how discrete distribution approximates to normal.