{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 16: Exponential Distribution, Memoryless Property\n", "\n", "\n", "## Stat 110, Prof. Joe Blitzstein, Harvard University\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Exponential Distribution\n", "\n", "### Description\n", "\n", "Real-valued distribution describing wait times, survival times. Rate parameter $\\lambda \\gt 0$. \n", "\n", "Continuous analog of the geometric distribution.\n", "\n", "Unique in that the exponential distribution has the memoryless property.\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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HTU0NHA4H3G43vF4vfD5f0HolSYJKpYJarYZWq4VGo4FarYZGo4FGo4HRaERK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\n+d2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"text/plain": [ "<matplotlib.figure.Figure at 0x1dfbab36198>" ] }, "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 expon\n", "\n", "%matplotlib inline\n", "\n", "plt.xkcd()\n", "\n", "_, ax = plt.subplots(figsize=(12,8))\n", "\n", "\n", "# seme Exponential parameters\n", "lambdas = [2.0, 1.5, 1.0, 0.5]\n", "\n", "# qualitative color scheme\n", "colors = ['#66c2a5', '#fc8d62', '#8da0cb', '#e78ac3']\n", "\n", "x = np.linspace(0, 4, 500)\n", "for i,l in enumerate(lambdas):\n", " pdf = expon.pdf(x, scale=1/l)\n", " ax.plot(x, pdf, color=colors[i], lw=3.2, label=r'$\\lambda = {}$'.format(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([-0.01, 2.0])\n", "ax.set_ylabel(r'$f(x)$')\n", "ax.set_yticks(np.arange(0,2.1,.2))\n", "\n", "# x-axis\n", "ax.set_xlim([0.0, 3.0])\n", "ax.set_xlabel(r'$x$')\n", "\n", "# x-axis tick formatting\n", "majorLocator = MultipleLocator(1)\n", "majorFormatter = FormatStrFormatter('%d')\n", "minorLocator = MultipleLocator(1)\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'Exponential PDF: $f(x) = \\lambda e^{-\\lambda x}$ for $x \\geq 0$')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Notation\n", "\n", "$X \\sim \\operatorname{Expo}(\\lambda)$\n", "\n", "### Parameters\n", "\n", "$\\lambda$ - rate parameter where $\\lambda \\gt 0$\n", "\n", "### Probability density function\n", "\n", "\\begin{align}\n", " f(x) &= \n", " \\begin{cases}\n", " \\lambda e^{-\\lambda x}, &\\text{ if } x \\ge 0 \\\\\n", " 0, &\\text{ otherwise }\n", " \\end{cases} \n", "\\end{align}\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Cumulative distribution function\n", "\n", "\\begin{align}\n", " F(x) &= \\int_{0}^{x} \\lambda e^{-\\lambda t} \\, dt \\\\\n", " &= \\lambda \\int_{0}^{x} e^{-\\lambda t} \\, dt &\\text{ let } u = -\\lambda t \\text{, } du = -\\lambda \\, dt \\\\\n", " &= \\int - e^{u} \\, du \\\\ \n", " &= - e^{u} \\\\\n", " &= \\left. - e^{-\\lambda t} \\right|_{0}^{x} \\\\\n", " &= \\boxed{ 1 - e^{-\\lambda x} }\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Standardized Exponential Distribution\n", "\n", "If we let $Y = \\lambda X$, then $Y \\sim \\operatorname{Expo}(1)$.\n", "\n", "You can compare this with the standardized Normal.\n", "\n", "Proof\n", "\n", "\\begin{align}\n", " P(Y \\le y) &= P\\left(X \\le \\frac{y}{\\lambda} \\right) \\\\\n", " &= 1 - e^{-\\lambda \\frac{y}{\\lambda}} &\\text{ just plugging } \\frac{y}{\\lambda} \\text{ into the CDF above} \\\\\n", " &= 1 - e^{-y} &\\text{ which is the CDF of } \\operatorname{Expo}(1) ~~~~ \\blacksquare \\\\\n", "\\end{align}\n", "\n", "We will next find the mean and variance of $\\operatorname{Expo}(1)$, and then derive the general case mean and variance afterwards." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean and variance of $\\operatorname{Expo}(1)$\n", "\n", "Let $Y \\sim \\operatorname{Expo}(1)$, find $\\mathbb{E}(Y)$ and $\\operatorname{Var}(Y)$.\n", "\n", "\\begin{align}\n", " \\mathbb{E}(Y) &= \\int_{0}^{\\infty} y\\,e^{-y}\\,dy & &\\text{ let } u = y \\text{, } du = dy \\\\\n", " & & &\\text{ and let } dv = e^{-y}\\,dy \\text{, } v = -e^{-y} \\\\\n", " &= \\underbrace{ \\left. -y e^{^y} \\right\\vert_{0}^{\\infty}}_{\\text{evaluates to }0} + \\underbrace{\\int_{0}^{\\infty} e^{-y}\\,dy}_{\\text{PDF of }\\operatorname{Expo}(1)} \\\\\n", " &= \\boxed{1} \\\\\n", " \\\\\\\\\n", " \\operatorname{Var}(Y) &= \\mathbb{E}(Y^2) - \\mathbb{E}Y ^2\\\\\n", " &= \\int_{0}^{\\infty} y^{2}\\,e^{-y}\\,dy \\,- 1^2 & &\\text{ let } u = y^{2} \\text{, } du = 2y\\,dy \\\\\n", " & & &\\text{ and let } dv = e^{-y}\\,dy \\text{, } v = -e^{-y} \\\\\n", " &= \\left. -y^{2}\\,e^{^y} \\right\\vert_{0}^{\\infty} + \\int_{0}^{\\infty} 2y\\,e^{-y}\\,dy \\,-1 \\\\\n", " &= 0 + 2 - 1 \\\\\n", " &= \\boxed{1}\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean and variance of $\\operatorname{Expo}(\\lambda)$\n", "\n", "We can derive the mean and variance of $\\operatorname{Expo}(\\lambda)$ from that of $\\operatorname{Expo}(1)$.\n", "\n", "From $Y = \\lambda X$ we have $X = \\frac{y}{\\lambda}$.\n", "\n", "\\begin{align}\n", " \\mathbb{E}(X) &= \\mathbb{E}\\left(\\frac{Y}{\\lambda}\\right) \\\\\n", " &= \\frac{1}{\\lambda} \\, \\mathbb{E}(Y) \\\\\n", " &= \\boxed{ \\frac{1}{\\lambda} } \\\\\n", " \\\\\\\\\n", " \\operatorname{Var}(X) &= \\operatorname{Var}\\left(\\frac{Y}{\\lambda}\\right) \\\\\n", " &= \\frac{1}{\\lambda^2} \\, \\operatorname{Var}(Y) \\\\\n", " &= \\boxed{ \\frac{1}{\\lambda^2} } \\\\\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Memorylessness Property\n", "\n", "If you have a random variable representing a wait-time (continuous), the memorylessness property means that no matter how long you have already waited, the probability that you will have to wait an _additional_ time $t$ is the same as if you were starting fresh from 0 (irrespective of the time you already spent waiting).\n", "\n", "Fact: $\\operatorname{Expo}(\\lambda)$ is the only distribution with the memorylessness property.\n", "\n", "\\begin{align}\n", " P(X \\ge s+t | X \\ge s) &= P(X \\ge t) \\\\\n", "\\end{align}\n", "\n", "The survival function is the random variable that describes how long something might live/exist, in constrast to that for a waiting time. In other words, $P(X \\ge s)$ is the probability that some object of interest _lasts longer than_ a continuous time $s$. \n", "\n", "\\begin{align}\n", " P(X \\ge s) &= 1 - P(X \\le s) \\\\\n", " &= 1 - (1 - e^{-\\lambda s}) \\\\\n", " &= e^{-\\lambda s} & \\quad \\text{ the survival function}\n", "\\end{align}\n", "\n", "And so using this survival function in an equation using the definition of conditional probability, we have:\n", "\n", "\\begin{align}\n", " P(X \\ge s+t | X \\ge s) &= \\frac{P(X \\ge s+t \\text{, }X \\ge s)}{P(X \\ge s)} \\\\\n", " &= \\frac{P(X \\ge s+t)}{P(X \\ge s)} & \\quad \\text{ since } P(X \\ge s) \\text{ is redundant} \\\\\n", " &= \\frac{e^{-\\lambda (s+t)}}{e^{-\\lambda s}} & \\quad \\text{ ratio of survival functions} \\\\\n", " &= e^{-\\lambda t} \\\\\n", " &= P(X \\ge t) & \\quad \\blacksquare\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Useful corollary of the Memorylessness Property\n", "\n", "This is a brief introduction to conditional expectation, which is just like conditional probability.\n", "\n", "Given $X \\sim \\operatorname{Expo}(\\lambda)$, what is the expected wait-time if we have already waited for some time $a$?\n", "\n", "\\begin{align}\n", " \\mathbb{E}(X | X \\gt a) &= a + \\mathbb{E}(X - a|X \\gt a) & \\quad \\text{ by linearity} \\\\\n", " &= a + \\frac{1}{\\lambda} & \\quad \\text{ by the memorylessness property}\n", "\\end{align}\n", "\n", "----" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "View [Lecture 16: Exponential Distribution | Statistics 110](http://bit.ly/2CxRIfh) 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": 1 }