{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Probability Distributions and the Central Limit Theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Markus Pfeil, Hochschule Ravensburg Weingarten\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we will visualize, in Python, a few important distributions that commonly appear in science and statistics. A more exhaustive list of statistical distributions can be found in the [stats](http://docs.scipy.org/doc/scipy/reference/stats.html) module of SciPy. \n", "\n", "At the end of this IPython Notebook we will demonstrate what is arguably the most famous and profound theorem in statistics: the Central Limit Theorem." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from __future__ import division\n", "\n", "import numpy as np\n", "import scipy.stats as stats\n", "import matplotlib.pyplot as plt\n", "from ipywidgets import interact, interactive, fixed, interact_manual\n", "import ipywidgets as widgets\n", "from IPython.display import display" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\mathbf{Uniform}$:The probability of observing each value with the same probability.\n", "\n", "* Example: Measurement with white noise" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "cb1dbe90a651454dbbc44a97b3cba1ba", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=5.0, description='mean', max=10.0), FloatSlider(value=5.0, description…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def func(mean,var, size): \n", " s = var*stats.uniform.rvs(size)+mean\n", " fig, ax = plt.subplots(1, 1)\n", " ax.hist(s, density=True, histtype='stepfilled', alpha=0.2)\n", " plt.show()\n", " \n", "interactive_plot = interact_manual(func, mean=(0.0,10.0), var=(0.0,10.0), size=(10,1000,10))\n", "display(interactive_plot)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Continuous Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\mathbf{GAUSSIAN (NORMAL)}$:\n", "$P(x;\\mu,\\sigma)=\\displaystyle \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp{\\displaystyle \\left( -\\frac{(x-\\mu)^2}{2 \\sigma^2} \\right) },\n", "\\hspace{1in} x \\in [-\\infty;\\infty]$\n", "\n", "* mean=$\\mu$, variance=$\\sigma^2$\n", "* This distribution appears as the large N limit of the binomial distribution and the Central Limit Theorem." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u=5 # mean\n", "s=1 # standard deviation\n", "x=np.arange(0,15,0.1)\n", "y=(1/(np.sqrt(2*np.pi*s*s)))*np.exp(-(((x-u)**2)/(2*s*s)))\n", "plt.plot(x,y,'-')\n", "plt.title('Gaussian: $\\mu$=%.1f, $\\sigma$=%.1f' % (u,s),fontsize=15)\n", "plt.xlabel('x',fontsize=15)\n", "plt.ylabel('Probability density',fontsize=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\mathbf{EXPONENTIAL}$:\n", "$P(x;k)=k e^{-kx}, \\hspace{1in} x \\in [0,\\infty], \\hspace{0.1in} k>0$\n", "\n", "* mean=$1/k$, variance=$1/k^2$\n", "* This distribution describes the time intervals in a homogeneous Poisson process." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k=0.4\n", "x=np.arange(0,15,0.1)\n", "y=k*np.exp(-k*x)\n", "plt.plot(x,y,'-')\n", "plt.title('Exponential: $k$ =%.2f' % k,fontsize=15)\n", "plt.xlabel('x',fontsize=15)\n", "plt.ylabel('Probability density',fontsize=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Central Limit Theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Take the mean of $n$ random samples from ANY arbitrary distribution with a well defined standard deviation $\\sigma$ and mean $\\mu$. As $n$ gets bigger the distribution of the sample mean will always converge to a Gaussian (normal) distribution with mean $\\mu$ and standard deviation $\\sigma/\\sqrt{n}$.\n", "\n", "Colloquially speaking, the theorem states that the average (or sum) of a set of random measurements will tend to a bell-shaped curve no matter the shape of the original meaurement distribution. This explains the ubiquity of the Gaussian distribution in science and statistics. We can demonstrate the Central Limit Thereom in Python by sampling from three different distributions: flat, exponential, and beta." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\mopfe\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n", " warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from functools import partial # provides capability to define function with partial arguments\n", "\n", "N=1000000 # number of times n samples are taken. Try varying this number.\n", "nobb=101 # number of bin boundaries on plots\n", "n=np.array([1,2,3,5,10,100]) # number of samples to average over\n", "\n", "exp_mean=3 # mean of exponential distribution\n", "a,b=0.7,0.5 # parameters of uniform distribution\n", "\n", "dist=[partial(np.random.random),partial(np.random.exponential,exp_mean),partial(np.random.uniform,a,b)]\n", "title_names=[\"Flat\", \"Exponential (mean=%.1f)\" % exp_mean, \"Uniform (a=%.1f, b=%.1f)\" % (a,b)]\n", "drange=np.array([[0,1],[0,10],[0,1]]) # ranges of distributions\n", "means=np.array([0.5,exp_mean,(a+b)/2]) # means of distributions\n", "var=np.array([1/12,exp_mean**2,1/12*(b-a)*(b-a)]) # variances of distributions\n", "\n", "binrange=np.array([np.linspace(p,q,nobb) for p,q in drange])\n", "ln,ld=len(n),len(dist)\n", "plt.figure(figsize=((ld*4)+1,(ln*2)+1))\n", "\n", "for i in range(ln): # loop over number of n samples to average over\n", " for j in range(ld): # loop over the different distributions\n", " plt.subplot(ln,ld,i*ld+1+j)\n", " plt.hist(np.mean(dist[j]((N,n[i])),1),binrange[j],normed=True)\n", " plt.xlim(drange[j])\n", " if j==0:\n", " plt.ylabel('n=%i' % n[i],fontsize=15) \n", " if i==0:\n", " plt.title(title_names[j], fontsize=15)\n", " else:\n", " clt=(1/(np.sqrt(2*np.pi*var[j]/n[i])))*np.exp(-(((binrange[j]-means[j])**2)*n[i]/(2*var[j])))\n", " plt.plot(binrange[j],clt,'r',linewidth=2) \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the graphs above the red curve is the predicted Gaussian distribution from the Central Limit Thereom. Notice that the rate of convergence of the sample mean to the Gaussian depends on the original parent distribution. Also, \n", "\n", "- the mean of the Gaussian distribution is the same as the original parent distribution,\n", "- the width of the Gaussian distribution scales as $1/\\sqrt{n}$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 1 }