{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 24: Gamma Distribution, Poisson Processes\n", "\n", "\n", "## Stat 110, Prof. Joe Blitzstein, Harvard University\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stirling's Approximation to the Factorial\n", "\n", "\\begin{align}\n", " n! &= n \\, (n-1) \\, (n -1) \\, \\dots \\, 1 \\\\\n", " &\\sim \\sqrt{2 \\pi n} \\, \\left( \\frac{n}{e} \\right)^{n}\n", "\\end{align}\n", "\n", "where $\\sim$ means that the ratio of the two number converges to 1 as $n$ approaches $\\infty$.\n", "\n", "This is fine when we are talking about $n \\in \\{1,2,3,\\dots\\}$, but have you ever wondered what $\\pi!$ is?\n", "\n", "For that, we need the Gamma function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gamma Function\n", "\n", "Just as an aside, the Beta and Gamma functions are closely related. The Gamma function should be amongst the Top 10 Functions of All Time (if there was ever such a list).\n", "\n", "\\begin{align}\n", " \\Gamma(a) &= \\int_{0}^{\\infty} x^a \\, e^{-x} \\, \\frac{dx}{x} \\quad \\text{for any real }a \\gt 0 \\\\\n", " &= \\int_{0}^{\\infty} x^{a-1} \\, e^{-x} \\, dx \\quad \\text{(alternately)}\n", "\\end{align}\n", "\n", "Note that if $a$ approaches 0 from the right, the $\\frac{dx}{x}$ is what drives that integral since $x^0 = 1$ and $e^{-0}=1$.\n", "\n", "But $\\int \\frac{dx}{x} = log(x)$ which blows up to $-\\infty$, which is why we restrict $a \\gt 0$.\n", "\n", "### Properties of the Gamma Function\n", "\n", "1. $\\Gamma(n) = (n-1)!$ where $n \\in \\mathbb{Z}^{+}$

\n", "1. $\\Gamma(x+1) = x \\, \\Gamma(x)$

\n", "1. $\\Gamma(\\frac{1}{2}) = \\sqrt{\\pi}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gamma Distribution\n", "\n", "How would we derive a PDF that is based on the Gamma distribution? \n", "\n", "_By normalizing the Gamma function._\n", "\n", "\\begin{align}\n", " 1 &= \\int_{0}^{\\infty} c \\, x^a \\, e^{-x} \\, \\frac{dx}{x} \\\\\n", " &= \\int_{0}^{\\infty} \\frac{1}{\\Gamma(a)} \\, x^a \\, e^{-x} \\, \\frac{dx}{x}\n", "\\end{align}\n", "\n", "And so the PDF for a Gamma distribution would be\n", "\n", "\\begin{align}\n", " \\operatorname{Gamma}(a,1) &= \\frac{1}{\\Gamma(a)} \\, x^a \\, e^{-x} \\, \\frac{dx}{x} \\quad \\text{for } x \\gt 0 \\\\\\\\\n", " \\\\\n", " \\text{More generally } Y &\\sim \\operatorname{Gamma}(a, \\lambda) \\\\\n", " \\text{Let } Y &= \\frac{X}{\\lambda} \\text{, where } X \\sim \\operatorname{Gamma}(a,1) \\\\\n", " \\rightarrow y &= \\frac{x}{\\lambda} \\\\\n", " x &= \\lambda \\, y \\\\\n", " \\frac{dx}{dy} &= \\lambda \\\\\n", " \\\\\n", " \\Rightarrow f_Y(y) &= f_X(x) \\, \\frac{dx}{dy} \\quad \\text{ transforming } X \\text{ to } Y \\\\\n", " &= \\frac{1}{\\Gamma(a)} \\, (\\lambda y)^a \\, e^{-\\lambda y} \\, \\frac{1}{\\lambda y} \\, \\lambda \\\\\n", " &= \\frac{1}{\\Gamma(a)} \\, (\\lambda y)^a \\, e^{-\\lambda y} \\, \\frac{1}{y} \\quad \\text{for } y \\gt 0\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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ZjDFWmXhUGcYYY7UC2Ycwhkwmc/sA54IFC6BSqTB37lwA9gc+k5OTERoaCl9f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JtEfBOOfcqL5YiiGLMwj45i9+7dmDx5Mh544AEsWbIEKpUK48ePx/PPP4+ioiLcfffdKCoqwoYN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dyL6tCusqD2vL1vJnm/+ML6z/Ak3upqzXeaNefn/p9/zT8X/i+NBxYaFZBJUrVnHDo5/GWZYe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\niYkJk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from matplotlib.ticker import (MultipleLocator, FormatStrFormatter,\n", " AutoMinorLocator)\n", "from scipy.stats import gamma\n", "\n", "%matplotlib inline\n", "\n", "plt.xkcd()\n", "\n", "_, ax = plt.subplots(figsize=(12,8))\n", "\n", "alpha_values = [1.,2.,3.,4.,5.,7.5,9.,0.5]\n", "lambda_values = [2.,2.,2.,1.,0.5,1.,1.,0.5]\n", "x = np.linspace(0, 20, 1000)\n", "\n", "# plot the distributions\n", "#fig, ax = plt.subplots(figsize=(12, 6))\n", "\n", "for a,l in zip(alpha_values, lambda_values):\n", " ax.plot(x, gamma.pdf(x, a, scale=l), lw=3.2, alpha=0.6, label=r'$\\alpha$={}, $\\lambda$={}'.format(a,l))\n", " \n", "# legend styling\n", "legend = ax.legend()\n", "for label in legend.get_texts():\n", " label.set_fontsize('large')\n", "for label in legend.get_lines():\n", " label.set_linewidth(1.5)\n", "\n", "# y-axis\n", "ax.set_ylim([0.0, 0.5])\n", "ax.set_ylabel(r'$f(x)$')\n", "\n", "# x-axis\n", "ax.set_xlim([0, 20.0])\n", "ax.set_xlabel(r'$x$')\n", "\n", "# x-axis tick formatting\n", "majorLocator = MultipleLocator(5.0)\n", "majorFormatter = FormatStrFormatter('%0.1f')\n", "minorLocator = MultipleLocator(1.0)\n", "ax.xaxis.set_major_locator(majorLocator)\n", "ax.xaxis.set_major_formatter(majorFormatter)\n", "ax.xaxis.set_minor_locator(minorLocator)\n", "\n", "ax.grid(color='grey', linestyle='-', linewidth=0.3)\n", "\n", "plt.suptitle(r'Gamma Distribution $f(x) = \\frac{1}{\\Gamma(\\alpha)} \\, (\\lambda x)^{\\alpha} \\, e^{-\\lambda x} \\, \\frac{1}{x}$')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "----" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Connecting the Gamma and Exponential, Poisson Distributions\n", "\n", "### Poisson Processes\n", "\n", "Recall Poisson processes, where the number of events happening in a certain time period $t$ is such that\n", "\n", "\\begin{align}\n", " N_t &= \\text{number of events occuring up to time }t \\\\\n", " &\\sim \\operatorname{Pois}(\\lambda, t)\n", "\\end{align}\n", "\n", "where the number of events occuring in disjoint time intervals are independent.\n", "\n", "Now earlier, we discussed how time $t$ is exponential. Consider $t_1$, the time until we observe the very first event.\n", "\n", "\\begin{align}\n", " P(t_1 \\gt t) &= P(N_t = 0) &\\quad \\text{by definition} \\\\\n", " &= \\frac{\\lambda^0 \\, e^{\\lambda t}}{0!} \\\\\n", " &= e^{\\lambda t} \\\\\n", " &= 1 - (1-e^{\\lambda t}) &\\quad \\text{1 - CDF of } \\operatorname{Expo}(\\lambda) \\\\\\\\\n", " \\\\ \n", " \\Rightarrow &\\text{time until first event } \\sim \\operatorname{Expo}(\\lambda)\n", "\\end{align}\n", "\n", "And so using this argument along with the memorylessness property, all of the other times between subsequent events $t_2, t_3, \\dots , t_n$ are also $\\operatorname{Expo}(\\lambda)$\n", "\n", "### Analogies: Geometric $\\rightarrow$ Negative binomial (discrete); Exponential $\\rightarrow$ Gamma (continuous)\n", "\n", "So the interarrival time for events in a Poisson process are i.i.d. $\\operatorname{Expo}(\\lambda)$.\n", "\n", "But what if we want to know $t_n$, the time of the $n^{th}$ arrival?\n", "\n", "\\begin{align}\n", " T_n &= \\sum_{i=1}^{n} X_1, X_2, \\dots , X_n &\\quad \\text{where } X_i \\text{ is i.i.d. } \\operatorname{Expo}(\\lambda) \\\\\\\\\n", " &\\sim \\operatorname{Gamma}(n, \\lambda) &\\quad \\text{ assuming } n \\text{ is an integer} \n", "\\end{align}\n", "\n", "Recall the relation between the geometric and negative binomial distributions:\n", "* In geometric $\\operatorname{Geom}(p)$, we count discrete time until $1^{st}$ success\n", "* In negative binomial $\\operatorname{NB}(n, p)$, we count discrete time until $n^{th}$ success ($\\sum_{i=1}^{n} X_i \\text{ where } X_i \\text{ i.i.d., } X_i \\sim \\operatorname{Geom}(\\lambda)$ )\n", "\n", "Well, there's is something analogous between the exponential and Gamma distributions:\n", "* In exponential $Expo(\\lambda)$, we count continuous time until $1^{st}$ success\n", "* In Gamma, we count continuous time until $n^{th}$ success ($\\sum_{i=1}^{n} X_i \\text{ where } X_i \\text{ i.i.d, } X_i \\sim \\operatorname{ Expo}(\\lambda)$ )\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Moments of Gamma\n", "\n", "#### $X \\sim \\operatorname{Gamma}(\\alpha, 1)$\n", "\n", "Let $X \\sim \\operatorname{Gamma}(\\alpha,1)$\n", "\n", "Directly using LOTUS:\n", "\n", "\\begin{align}\n", " \\mathbb{E}(X^c) &= \\int_{0}^{\\infty} \\frac{1}{\\Gamma(a)} \\,x^c \\, x^{\\alpha} \\, e^{-x} \\, \\frac{dx}{x} \\\\\n", " &= \\int_{0}^{\\infty} \\frac{1}{\\Gamma(\\alpha)} \\, x^{a+c} \\, e^{-x} \\, \\frac{dx}{x} \\\\\n", " &= \\frac{\\Gamma(\\alpha+c)}{\\Gamma(\\alpha)} &\\quad \\text{, where } \\alpha+x \\gt 0 \\\\\\\\\n", " \\\\\n", " 1^{st} \\text{ moment (mean) of } \\operatorname{Gamma}(n,1) &= \\mathbb{E}(X) \\\\\n", " &= \\frac{\\Gamma(\\alpha+1)}{\\Gamma(\\alpha)} \\\\\n", " &= \\frac{\\alpha \\, \\Gamma(\\alpha)}{\\Gamma(\\alpha)} \\\\\n", " &= \\boxed{ \\alpha } \\\\\\\\\n", " \\\\\n", " 2^{nd} \\text{ moment } \\operatorname{Gamma}(n,1) &= \\mathbb{E}(X^2) \\\\\n", " &= \\frac{\\Gamma(\\alpha+2)}{\\Gamma(\\alpha)} \\\\\n", " &= \\frac{(\\alpha+1) \\, \\Gamma(\\alpha+1)}{\\Gamma(\\alpha)} \\\\\n", " &= \\frac{(\\alpha+1)\\alpha \\, \\Gamma(\\alpha)}{\\Gamma(\\alpha)} \\\\\n", " &= \\alpha^2 + \\alpha \\\\\n", " \\\\\n", " \\Rightarrow \\operatorname{Var} \\text{ of } \\operatorname{Gamma}(n,1) &= \\mathbb{E}(X^2) - \\left( \\mathbb{E}(X)^2 \\right) \\\\\n", " &= \\alpha^2 + \\alpha - \\alpha^2 \\\\\n", " &= \\boxed{ \\alpha }\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $X \\sim \\operatorname{Gamma}(\\alpha, \\lambda)$\n", "\n", "Applying what we know from the case of above and using LOTUS:\n", "\n", "\\begin{align}\n", " \\mathbb{E}(X^c) &= \\int_{0}^{\\infty} \\frac{1}{\\Gamma(\\alpha)} \\,x^c \\, (\\lambda x)^{\\alpha} \\, e^{-\\lambda x} \\, \\frac{dx}{\\lambda x} \\\\\n", " &= \\int_{0}^{\\infty} \\frac{1}{\\Gamma(\\alpha)} \\, x^{\\alpha+c} \\, \\lambda^{\\alpha} \\, e^{-\\lambda x} \\, \\frac{dx}{\\lambda \\, x} \\\\\n", " &= \\int_{0}^{\\infty} \\frac{1}{\\Gamma(\\alpha)} \\, (\\lambda \\, x)^{\\alpha+c} \\, e^{-\\lambda x} \\, \\frac{dx}{\\lambda \\, x} \\, \\frac{1}{\\lambda^c} \\\\\n", " &= \\frac{\\Gamma(\\alpha+c)}{\\Gamma(\\alpha) \\, \\lambda^c} &\\quad \\text{, where } \\alpha+x \\gt 0 \\\\\\\\\n", " \\\\\n", " 1^{st} \\text{ moment (mean) of } \\operatorname{Gamma}(\\alpha,\\lambda) &= \\mathbb{E}(X) \\\\\n", " &= \\frac{\\Gamma(\\alpha+1)}{\\Gamma(\\alpha) \\, \\lambda} \\\\\n", " &= \\frac{\\alpha \\, \\Gamma(\\alpha)}{\\Gamma(\\alpha) \\, \\lambda} \\\\\n", " &= \\boxed{ \\frac{\\alpha}{\\lambda} } \\\\\\\\\n", " \\\\\n", " 2^{nd} \\text{ moment } \\operatorname{Gamma}(\\alpha,\\lambda) &= \\mathbb{E}(X^2) \\\\\n", " &= \\frac{\\Gamma(\\alpha+2)}{\\Gamma(\\alpha) \\, \\lambda^2} \\\\\n", " &= \\frac{(\\alpha+1) \\, \\Gamma(\\alpha+1)}{\\Gamma(\\alpha) \\, \\lambda^2} \\\\\n", " &= \\frac{(\\alpha+1)\\alpha \\, \\Gamma(\\alpha)}{\\Gamma(\\alpha) \\, \\lambda^2} \\\\\n", " &= \\frac{(\\alpha+1)\\alpha}{\\lambda^2} \\\\\n", " \\\\\n", " \\Rightarrow \\operatorname{Var} \\text{ of } \\operatorname{Gamma}\\alpha,\\lambda) &= \\mathbb{E}(X^2) - \\left( \\mathbb{E}(X)^2 \\right) \\\\\n", " &= \\frac{(\\alpha+1)\\alpha}{\\lambda^2} - \\left( \\frac{\\alpha}{\\lambda} \\right)^2 \\\\\n", " &= \\frac{\\alpha + \\alpha^2 - \\alpha^2}{\\lambda^2} \\\\\n", " &= \\boxed{ \\frac{\\alpha}{\\lambda^2} }\n", "\\end{align}\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "View [Lecture 24: Gamma distribution and Poisson process | Statistics 110](http://bit.ly/2CyadAf) on YouTube." ] } ], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }