{ "metadata": { "name": "", "signature": "sha256:44b93aa8ba921469a7ce4488f8383e0d30de14ced16aeaa7fca61a9a4b12880f" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "# special IPython command to prepare the notebook for matplotlib\n", "%matplotlib inline \n", "\n", "import numpy as np\n", "import scipy.stats as stats\n", "import matplotlib.pyplot as plt\n", "\n", "import pandas as pd\n", "import numpy as np\n", "\n", "# special matplotlib argument for improved plots\n", "from matplotlib import rcParams\n", "\n", "#colorbrewer2 Dark2 qualitative color table\n", "dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),\n", " (0.8509803921568627, 0.37254901960784315, 0.00784313725490196),\n", " (0.4588235294117647, 0.4392156862745098, 0.7019607843137254),\n", " (0.9058823529411765, 0.1607843137254902, 0.5411764705882353),\n", " (0.4, 0.6509803921568628, 0.11764705882352941),\n", " (0.9019607843137255, 0.6705882352941176, 0.00784313725490196),\n", " (0.6509803921568628, 0.4627450980392157, 0.11372549019607843)]\n", "\n", "rcParams['figure.figsize'] = (10, 6)\n", "rcParams['figure.dpi'] = 150\n", "rcParams['axes.color_cycle'] = dark2_colors\n", "rcParams['lines.linewidth'] = 2\n", "rcParams['axes.facecolor'] = 'white'\n", "rcParams['font.size'] = 14\n", "rcParams['patch.edgecolor'] = 'white'\n", "rcParams['patch.facecolor'] = dark2_colors[0]\n", "rcParams['font.family'] = 'StixGeneral'" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Recall from from lab last week 09/26/2014\n", "\n", "Previously discussed: \n", "\n", "* urllib2 - reads in HTML\n", "* BeautifulSoup - use to parse HTML and XML code\n", " * Reddit\n", "* JSON examples\n", " * World Cup" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Today, we will discuss the following:\n", "\n", "* Random variables and probability distributions\n", "* Central Limit Theorem (CLT)\n", "\n", "\n", " Download this notebook from Github \n", "\n", "---\n", "\n", "Some notes extracted from [Mickey Atwal, Cold Spring Harbor Laboratory](http://nbviewer.ipython.org/url/atwallab.cshl.edu/teaching/distributions.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Random Variables and Probability Distributions\n", "\n", "A [random variable](http://en.wikipedia.org/wiki/Random_variable) is a variable that takes on a set of possible values (**discrete** or **continuous**) and is subject to *randomness*. Each possible value the random variable can take on is associated with a probability. The possible values the random variable can take on and the associated probabilities is known as [probability distribution](http://en.wikipedia.org/wiki/Probability_distribution). \n", "\n", "We will start by looking at a few probability distributions in in the `scipy.stats` [module](http://docs.scipy.org/doc/scipy/reference/stats.html). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discrete distributions \n", "\n", "Discrete probability distributions are also known as [probability mass functions](http://en.wikipedia.org/wiki/Probability_mass_function). Examples include the [Bernoulli distribution](http://en.wikipedia.org/wiki/Bernoulli_distribution), the [binomial distribution](http://en.wikipedia.org/wiki/Binomial_distribution), the [Poisson distribution]() and the [geometric distribution](http://en.wikipedia.org/wiki/Geometric_distribution). \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Binomial\n", "\n", "A random variable $X$ that has a binomial distribution represents the number of successes in a sequence of $n$ independent yes/no trials, each of which yields success with probability $p$. \n", "\n", "$$P(X = k) = \\displaystyle \\left(\n", "\\frac{n!}{k!(n-k)!}\n", "\\right)\n", "p^k (1-p)^{n-k}$$\n", "\n", "\n", "* E(X) = $np$, Var(X) = $np(1-p)$\n", "* Example: what is the probability of getting 2 heads out of 10 flips of a fair coin?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Let's look at the help file for the stats.binom function\n", "# stats.binom?" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "n = 10\n", "p = 0.3\n", "k = np.arange(0,11) # plot all values between 0 and 10\n", "y = stats.binom.pmf(k, n, p)\n", "print y" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 2.82475249e-02 1.21060821e-01 2.33474440e-01 2.66827932e-01\n", " 2.00120949e-01 1.02919345e-01 3.67569090e-02 9.00169200e-03\n", " 1.44670050e-03 1.37781000e-04 5.90490000e-06]\n" ] } ], "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(k, y, 'o-')\n", "plt.title('Binomial: n=%i , p=%.2f' % (n,p),fontsize=15)\n", "plt.xlabel('Number of successes')\n", "plt.ylabel('Probability of successes', fontsize=15)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAGQCAYAAAAuv128AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAWipO0CGlEWjAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "# your turn\n", "\n", "# Try changing p to p = 0.6.\n", "# Try plotting values values larger than 10." ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's simulate binomial random variables using `stats.binom.rvs`" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# stats.binom?" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "data = stats.binom.rvs(n = 10, p = 0.3, size = 10000)\n", "print \"Mean: %g\" % np.mean(data)\n", "print \"SD: %g\" % np.std(data, ddof=1)\n", "\n", "plt.figure()\n", "plt.hist(data, bins = 10, normed = True)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"density\")\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Mean: 3.0091\n", "SD: 1.46616\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAGHCAYAAAAwbG+fAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Poisson \n", "\n", "A random variable $X$ that has a Poisson distribution represents the number of events occurring in a fixed time interval with a rate parameters $\\lambda$. \n", "\n", "$$P(X = k) = \\frac{\\lambda^k e^{-\\lambda}}{k!} $$\n", "\n", "* E(X) = $\\lambda$, Var(X) = $\\lambda$\n", "* Example: what is probability of observing 4 accidents at an intersections in a day given the rate of accidents is 2 per day? " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Let's look at the help file for the stats.binom function\n", "# stats.poisson?" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 30 }, { "cell_type": "code", "collapsed": false, "input": [ "lam = 2 # rate parameter lambda\n", "n = np.arange(0, 11)\n", "y = stats.poisson.pmf(n, lam)\n", "print y" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 1.35335283e-01 2.70670566e-01 2.70670566e-01 1.80447044e-01\n", " 9.02235222e-02 3.60894089e-02 1.20298030e-02 3.43708656e-03\n", " 8.59271640e-04 1.90949253e-04 3.81898506e-05]\n" ] } ], "prompt_number": 31 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(n, y, 'o-')\n", "plt.title('Poisson: $\\lambda$ =%i' % lam)\n", "plt.xlabel('Number of accidents')\n", "plt.ylabel('Probability of number of accidents')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAGSCAYAAABjd/y3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "# your turn\n", "\n", "# try changing the rate parameters to 1. \n", "# Try changing the rate parameter to 8. \n", "# stats.poisson?" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's simulate Poisson random variables using `stats.poisson.rvs`" ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = stats.poisson.rvs(mu = 2, loc = 0, size = 1000)\n", "print \"Mean: %g\" % np.mean(data)\n", "print \"SD: %g\" % np.std(data, ddof=1)\n", "\n", "plt.figure()\n", "plt.hist(data, bins = 9, normed = True)\n", "plt.xlim(0, 10)\n", "plt.xlabel(\"Number of accidents\")\n", "plt.title(\"Simulating Poisson Random Variables\")\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Mean: 2.007\n", "SD: 1.41526\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAl4AAAGRCAYAAAC0d716AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Continuous distributions\n", "\n", "Continuous probability distributions also known as [probability density functions](http://en.wikipedia.org/wiki/Probability_density_function) are functions that take on continuous values (e.g. values on the real line). Examples include the [normal distribution](http://en.wikipedia.org/wiki/Normal_distribution), the [exponential distribution](http://en.wikipedia.org/wiki/Exponential_distribution) and the [beta distribution](http://en.wikipedia.org/wiki/Beta_distribution). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "#### Normal (or Gaussian)\n", "\n", "The normal distribution is a continuous distribution or a function that can take on values anywhere on the real line. The normal distribution is parameterized by two parameters: the mean of the distribution $\\mu$ and the variance $\\sigma^2$. \n", "\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", "\n", "* E(X) = $\\mu$, Var(X) = $\\sigma^2$\n", "* This distribution appears as the large n limit of the binomial distribution which you saw in Homework 2 and the **Central Limit Theorem** which we will discuss in a little bit." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# your turn \n", "# plot the pdf of a normal distribution with mean = 0 and \n", "# standard deviation = 1\n", "\n", "mu = 0 # mean\n", "sigma = 1 # standard deviation\n", "x = np.arange(-5,5,0.1)\n", "\n", "y = stats.norm.pdf(x, 0, 1)\n", "plt.plot(x, y)\n", "plt.title('Normal: $\\mu$=%.1f, $\\sigma^2$=%.1f' % (mu, sigma))\n", "plt.xlabel('x')\n", "plt.ylabel('Probability density')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAm0AAAGXCAYAAADh6mdcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npwdHgwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 35 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Beta \n", "\n", "The beta distribution is a continuous distribution which can take values between 0 and 1. This distribution is parameterized by two shape parameters $\\alpha$ and $\\beta$. \n", "\n", "$$P(x;\\alpha,\\beta)=\\displaystyle \\frac{\\Gamma(\\alpha+\\beta)}{\\Gamma(\\alpha) \\Gamma(\\beta)}x^{\\alpha-1}(1-x)^{\\beta-1}, \\hspace{1in} x \\in [0;1], \\hspace{0.1in} \\alpha>0, \\hspace{0.1in}\\beta>0$$\n", "\n", "* E(X) = $\\displaystyle \\frac{\\alpha}{\\alpha+\\beta}$, Var(X) = $\\displaystyle \\frac{\\alpha \\beta}{(\\alpha + \\beta)^2(\\alpha + \\beta +1)}$\n", "* This distribution appears often in population genetics and Bayesian inference." ] }, { "cell_type": "code", "collapsed": false, "input": [ "a = 0.5\n", "b = 0.5\n", "x = np.arange(0.01, 1, 0.01)\n", "y = stats.beta.pdf(x, a, b)\n", "plt.plot(x, y)\n", "plt.title('Beta: a=%.1f, b=%.1f' % (a,b))\n", "plt.xlabel('x')\n", "plt.ylabel('Probability density')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAmsAAAGRCAYAAAA6rfQGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/NY/YHzDogAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [ "# your turn\n", "\n", "# Try changing alpha = 0.8, beta = 0.5\n", "# Try changing alpha = 2, beta = 6\n", "# Try changing alpha = 4, beta = 2\n", "# Try changing alpha = 1, beta = 1\n", "\n", "# What do you notice when alpha and beta are both less than 1 \n", "# compared to both bigger than 1? " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exponential \n", "\n", "The exponential distribution represents a process in which events occur continuously and independently at a constant average rate. \n", "\n", "$$P(x;\\lambda)= \\lambda e^{-\\lambda x}, \\hspace{1in} x \\in [0,\\infty], \\hspace{0.1in} \\lambda > 0$$\n", "\n", "* E(X) = $1/\\lambda$, Var(X) = $1/\\lambda^2$\n", "* Example: The time to failure of a light bulb can be described by an exponential distribution with rate parameter $\\lambda$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "lam = 0.5\n", "x = np.arange(0, 15, 0.1)\n", "y = lam * np.exp(-lam * x) # could also use stats.expon.pdf\n", "plt.plot(x,y)\n", "plt.title('Exponential: $\\lambda$ =%.2f' % lam)\n", "plt.xlabel('x')\n", "plt.ylabel('Probability density')\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAGUCAYAAABulbWIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJEmSJEmSpEP6/2QmgQ/gZdKsAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's simulate exponential random variables using `stats.expon.rvs`" ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = stats.expon.rvs(scale = 2, size = 1000)\n", "print \"Mean: %g\" % np.mean(data)\n", "print \"SD: %g\" % np.std(data, ddof=1)\n", "\n", "plt.figure()\n", "plt.hist(data, bins = 20, normed = True)\n", "plt.xlim(0, 15)\n", "plt.title(\"Simulating Exponential Random Variables\")\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Mean: 2.0309\n", "SD: 1.96152\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAF/CAYAAACVJ7fPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIkSZIkqa39fzgVSr77qcF4AAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 39 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Histogram of the means of datasets with 100 values\n", "\n", "Now we will generate 1000 datasets each with 100 values drawn from an exponential distribution with $\\lambda$ = 0.5. We will compute the mean of each dataset and store them in an array of length 1000. \n", "\n", "* Compute the mean of the means and the standard deviation of the means\n", " * Print them to the screen. \n", "* Draw a boxplot of the means\n", "* Draw a histogram of the means" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Generate N = 1000 data sets of size 100 numbers drawn from an \n", "# exponential distribution (lambda = 0.5)\n", "data = stats.expon.rvs(scale=2, size = (1000, 100))\n", "\n", "# Compute sample mean for each N datasets\n", "sample_means = np.mean(data, axis = 1)\n", " \n", "print 'The mean of the means is: ', np.mean(sample_means)\n", "print 'The standard deviation of the means is: ', np.std(sample_means, ddof=1) \n", "plt.figure()\n", "plt.boxplot(sample_means)\n", "plt.figure()\n", "plt.hist(sample_means, normed=True)\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The mean of the means is: 1.99487250175\n", "The standard deviation of the means is: 0.198096906745\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlEAAAF1CAYAAADIqb9jAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nD5qopWY5nc0KAAAAAElFTkSuQmCC\n", "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAF1CAYAAADbfv+XAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAAAAAAAArpj/D8Q8jLuxZ8XCAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Central Limit Theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Take the mean of $n$ random samples $X_1, \\ldots, X_n$ from ANY arbitrary distribution with a well defined standard deviation $\\sigma$ and mean $\\mu$. As $n$ gets bigger the distribution of the sample mean $\\bar{X}$ will always converge to a Gaussian (normal) distribution with mean $\\mu$ and standard deviation $\\sigma/\\sqrt{n}$.\n", "\n", "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. We can demonstrate the Central Limit Thereom in Python by sampling from the exponential distribution. \n", "\n", "We will generate $N$ datasets of $n$ = 20 numbers drawn from an exponential distribution with $\\lambda = 1/2$. Then, we will draw a histogram of the sample means of the N datasets. \n", "\n", "On the same graph, draw the **pdf** of the normal distribution using the **mean of means** and **sample standard deviation of the mean**. We will make 3 graphs, for $N$ = 100, 1000, 10000 and notice that the distribution starts to approach a Normal distribution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "n = 20 \n", "for N in [100, 1000, 10000]:\n", " data = stats.expon.rvs(scale = 2, size=(N, n))\n", " sample_means = np.mean(data, axis=1) \n", "\n", " mu = np.mean(sample_means)\n", " sig = np.std(sample_means, ddof=1)\n", "\n", " plt.figure()\n", " plt.hist(sample_means, bins=20, normed=True)\n", " x = np.linspace(0, 4, 100)\n", " y = stats.norm.pdf(x, loc=mu, scale=sig)\n", " plt.plot(x, y, color = 'r')\n", " plt.title('Distribution of sample means using N=%i datasets' % N)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAF/CAYAAAB65dzxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSZIkSZIkSZIkSZIkvaFHOcZZrTwl2WAAAAAASUVORK5CYII=\n", "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAF/CAYAAAB65dzxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nj2ygg0AAAAAASUVORK5CYII=\n", "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlQAAAF/CAYAAACPG1dBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAAAAAAAAAAAAAAAAAAB+6R63Ae2bpn7LwwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate variance as the number of data sets $N$ increases\n", "\n", "The CLT states: \n", "\n", "> Take the mean of $n$ random samples $X_1, \\ldots, X_n$ from ANY arbitrary distribution with a well defined standard deviation $\\sigma$ and mean $\\mu$. As $n$ gets bigger the distribution of the sample mean $\\bar{X}$ will always converge to a Gaussian (normal) distribution with mean $\\mu$ and standard deviation $\\sigma/\\sqrt{n}$.\n", "\n", "This means that if $X \\sim Exponential(\\lambda)$ where $\\lambda$, then, \n", "\n", "$$ \\bar{X} \\sim Normal(\\mu, \\frac{\\sigma^2}{n} ) $$\n", "\n", "where $\\mu = 1/\\lambda$ and $\\sigma^2 = 1/\\lambda^2$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "n = 100\n", "\n", "for N in [100, 1000, 10000]:\n", " data = stats.expon.rvs(scale = 2, size=(N, n))\n", " sample_means = np.mean(data, axis=1) \n", "\n", " mu = np.mean(sample_means)\n", " sig = np.std(sample_means, ddof=1)\n", "\n", " print 'Standard deviation of simulated distribution: %g' % sig\n", " print 'Standard deviation using CLT: %g' % np.sqrt( 4 / float(n))\n", " print " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Standard deviation of simulated distribution: 0.205547\n", "Standard deviation using CLT: 0.2\n", "\n", "Standard deviation of simulated distribution: 0.200937\n", "Standard deviation using CLT: 0.2\n", "\n", "Standard deviation of simulated distribution: 0.200404" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Standard deviation using CLT: 0.2\n", "\n" ] } ], "prompt_number": 42 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# What happens if we increase $n$ and fix $N$? \n", "\n", "Now, generate $N = 1000$ datasets of $n$ numbers drawn from an exponential distribution with $\\lambda = 1/2$. Then, we will draw a histogram of the sample means of the N datasets as $n$ varies from 10, 100, 1000. \n", "\n", "On the same graph, draw the **pdf** of the normal distribution using the **mean of means** and **sample standard deviation of the mean**. We will make 3 graphs, for $n$ = 10, 100, 1000 and notice that the distribution starts to approach a Normal distribution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 1000 \n", "for n in [10, 100, 1000]:\n", " data = stats.expon.rvs(scale = 2, size=(N, n))\n", " sample_means = np.mean(data, axis=1) \n", "\n", " mu = np.mean(sample_means)\n", " sig = np.std(sample_means, ddof=1)\n", "\n", " plt.figure()\n", " plt.hist(sample_means, bins=20, normed=True)\n", " x = np.linspace(0, 4, 100)\n", " y = stats.norm.pdf(x, loc=mu, scale=sig)\n", " plt.plot(x, y, color = 'r')\n", " plt.title('Distribution of sample means using N=%i datasets of size n=%i datasets' % (N, n))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAF/CAYAAAB65dzxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nERERERERERERERERkQbk/wHmL2hFCkTI5QAAAABJRU5ErkJggg==\n", "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAAF/CAYAAAB65dzxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n", "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAk8AAAF/CAYAAABQVS1eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimate variance of as the sample size $n$ increases" ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 1000\n", "\n", "for n in [10, 100, 1000]:\n", " data = stats.expon.rvs(scale = 2, size=(N, n))\n", " sample_means = np.mean(data, axis=1) \n", "\n", " mu = np.mean(sample_means)\n", " sig = np.std(sample_means, ddof=1)\n", "\n", " print 'Standard deviation of simulated distribution: %g' % sig\n", " print 'Standard deviation using CLT: %g' % np.sqrt( 4 / float(n))\n", " print " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Standard deviation of simulated distribution: 0.62856\n", "Standard deviation using CLT: 0.632456\n", "\n", "Standard deviation of simulated distribution: 0.197999\n", "Standard deviation using CLT: 0.2\n", "\n", "Standard deviation of simulated distribution: 0.0637199" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "Standard deviation using CLT: 0.0632456\n", "\n" ] } ], "prompt_number": 44 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 44 } ], "metadata": {} } ] }