{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "# Distribution Functions\n", "\n", "\n", "![image.png](./images/author.png)\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Function Definition\n", "\n", "The following function will be used to show the different distributions functions\n", "\n", "- Normal distribution\n", "- Exponential distribution\n", "- T-distribution\n", "- F-distribution\n", "- Logistic distribution\n", "- Lognormal distribution\n", "- Uniform distribution\n", "- Binomial distribution\n", "- Poisson distribution" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T07:53:04.879358Z", "start_time": "2020-05-08T07:53:03.541785Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "# Note: here I use the iPython approach, which is best suited for interactive work\n", "%pylab inline\n", "from scipy import stats\n", "matplotlib.rcParams.update({'font.size': 18})" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T07:53:30.382207Z", "start_time": "2020-05-08T07:53:30.376345Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "x = linspace(-10,10,201)\n", "def showDistribution(d1, d2, tTxt, xTxt, yTxt, legendTxt, xmin=-10, xmax=10):\n", " '''Utility function to show the distributions, and add labels and title.'''\n", " plot(x, d1.pdf(x))\n", " if d2 != '':\n", " plot(x, d2.pdf(x), 'r')\n", " legend(legendTxt)\n", " xlim(xmin, xmax)\n", " title(tTxt)\n", " xlabel(xTxt)\n", " ylabel(yTxt)\n", " show() " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Normal distribution\n", "\n", "\n", "Carl Friedrich Gauss discovered the normal distribution in 1809 as a way to rationalize the method of least squares.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The standard normal distribution is a special case when $\\mu=0$ and $\\sigma =1$, and it is described by this probability density function:\n", "\n", "$$\n", "\\varphi(x) = \\frac 1{\\sqrt{2\\pi}}e^{- \\frac 12 x^2}\n", "$$\n", "\n", "- The factor $1/\\sqrt{2\\pi}$ in this expression ensures that the total area under the curve $\\varphi(x)$ is equal to one. \n", "- The factor $1/2$ in the exponent ensures that the distribution has unit variance (i.e., the variance is equal to one), and therefore also unit standard deviation. \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "![image.png](./images/normal_distrisbution.png)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T07:53:35.175379Z", "start_time": "2020-05-08T07:53:35.024690Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "showDistribution(stats.norm, stats.norm(loc=2, scale=4),\n", " 'Normal Distribution', 'Z', 'P(Z)','')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Exponential distribution\n", "The probability density function (pdf) of an exponential distribution is\n", "\n", "$$ f(x;\\lambda) = \\begin{cases}\n", "\\frac{1}{\\beta} e^{-\\frac{1}{\\beta} x} & x \\ge 0, \\\\\n", "0 & x < 0.\n", "\\end{cases}$$\n", "\n", "$\\beta$ is the scale parameter. Here $\\frac{1}{\\beta}$ is often called the **rate parameter**." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T18:14:21.960710Z", "start_time": "2020-05-08T18:14:21.814346Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xs = range(10)\n", "ys = [exp(-i) for i in xs]\n", "ys2 = [1/2*exp(-1/2*i) for i in xs]\n", "ys4 = [1/4*exp(-1/4*i) for i in xs]\n", "plt.plot(xs, ys, label = 'beta = 1')\n", "plt.plot(xs, ys2, label = 'beta = 2')\n", "plt.plot(xs, ys4, label = 'beta = 4')\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T08:51:37.852517Z", "start_time": "2020-05-08T08:51:37.708881Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Exponential distribution\n", "showDistribution(stats.expon(loc=0, scale = 1), stats.expon(loc=0, scale=4),\n", " 'Exponential Distribution', 'X', 'P(X)',['scale = 1', 'scale = 4'])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Students' T-distribution\n", "\n", "William Sealy Gosset" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let $ X_1, \\ldots, X_n $ be independent and identically distributed as $N(\\mu, \\sigma^2)$, i.e. this is a sample of size $n$ from a normally distributed population with expected mean value $\\mu $ and variance $\\sigma^2$.\n", "\n", "- Let $ \\bar X = \\frac 1 n \\sum_{i=1}^n X_i $ be the sample mean \n", "- let $ S^2 = \\frac 1 {n-1} \\sum_{i=1}^n (X_i - \\bar X)^2 $ be the sample variance. \n", "\n", "Then the random variable $ \\frac{ \\bar X - \\mu } { \\sigma /\\sqrt{n}} $ has a standard normal distribution (i.e. normal with expected mean 0 and variance 1), \n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The random variable $ \\frac{ \\bar X - \\mu} {S /\\sqrt{n}}, $ has a Student's **t**-distribution with $n - 1$ degrees of freedom.\n", "- where $S$ has been substituted for $\\sigma$.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Student's t-distribution has the **probability density function** given by\n", "\n", "$f(t) = \\frac{\\Gamma(\\frac{\\nu+1}{2})} {\\sqrt{\\nu\\pi}\\,\\Gamma(\\frac{\\nu}{2})} \\left(1+\\frac{t^2}{\\nu} \\right)^{\\!-\\frac{\\nu+1}{2}},\\!$\n", "\n", "where $\\nu$ is the number of degrees of freedom and $\\Gamma$ is the **gamma function**. \n", "\n", "This may also be written as\n", "\n", "$f(t) = \\frac{1}{\\sqrt{\\nu}\\,\\mathrm{B} (\\frac{1}{2}, \\frac{\\nu}{2})} \\left(1+\\frac{t^2}{\\nu} \\right)^{\\!-\\frac{\\nu+1}{2}}\\!,$\n", "\n", "where B is the **Beta function**. \n", "\n", "As the number of degrees of freedom grows, the t-distribution approaches the normal distribution with mean 0 and variance 1. \n", "\n", "For this reason ${\\nu}$ is also known as the normality parameter." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T08:11:16.326872Z", "start_time": "2020-05-08T08:11:16.153207Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# ... with 4, and with 10 degrees of freedom (DOF)\n", "plot(x, stats.norm.pdf(x), 'g')\n", "showDistribution(stats.t(4), stats.t(10),\n", " 'T-Distribution', 'X', 'P(X)',['normal', 't=4', 't=10'])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## F-distribution\n", "\n", "If a **random variable** X has an F-distribution with parameters d 1 and d 2, we write X ~ F(d1, d2). Then the **probability density function** (pdf) for X is given by\n", "\n", "$$\n", "\\begin{align}\n", "f(x; d_1,d_2) &= \\frac{\\sqrt{\\frac{(d_1x)^{d_1}\\,\\,d_2^{d_2}} {(d_1x+d_2)^{d_1+d_2}}}} {x\\,\\mathrm{B}\\!\\left(\\frac{d_1}{2},\\frac{d_2}{2}\\right)} \\\\\n", "&=\\frac{1}{\\mathrm{B}\\!\\left(\\frac{d_1}{2},\\frac{d_2}{2}\\right)} \\left(\\frac{d_1}{d_2}\\right)^{\\frac{d_1}{2}} x^{\\frac{d_1}{2} - 1} \\left(1+\\frac{d_1}{d_2}\\,x\\right)^{-\\frac{d_1+d_2}{2}}\n", "\\end{align}\n", "$$\n", "\n", "for real number x > 0. Here $\\mathrm{B}$ is the beta function. In many applications, the parameters d 1 and d 2 are positive integers, but the distribution is well-defined for positive real values of these parameters.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "![image.png](./images/normal2.png)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T08:31:29.244380Z", "start_time": "2020-05-08T08:31:29.096417Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# ... with (3,4) and (10,15) DOF\n", "showDistribution(stats.f(3,4), stats.f(10,15),\n", " 'F-Distribution', 'F', 'P(F)',['(3,4) DOF', '(10,15) DOF'])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Uniform distribution" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "showDistribution(stats.uniform,'' ,\n", " 'Uniform Distribution', 'X', 'P(X)','')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Logistic distribution\n", "\n", "\n", "$$\n", "\\begin{align}\n", "f(x; \\mu,s) & = \\frac{e^{-(x-\\mu)/s}} {s\\left(1+e^{-(x-\\mu)/s}\\right)^2} \\\\[4pt]\n", "& =\\frac{1}{s\\left(e^{(x-\\mu)/(2s)}+e^{-(x-\\mu)/(2s)}\\right)^2} \\\\[4pt]\n", "& =\\frac{1}{4s} \\operatorname{sech}^2\\left(\\frac{x-\\mu}{2s}\\right).\n", "\\end{align}\n", "$$\n", "\n", "Because this function can be expressed in terms of the square of the hyperbolic function \"sech\", it is sometimes referred to as the sech-square(d) distribution.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "![image.png](./images/normal3.png)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T08:40:42.770532Z", "start_time": "2020-05-08T08:40:42.626077Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "showDistribution(stats.norm, stats.logistic,\n", " 'Logistic Distribution', 'X', 'P(X)',['Normal', 'Logistic'])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Lognormal distribution\n", "\n", "A positive random variable X is log-normally distributed if the logarithm of X is normally distributed, $\\ln(X) \\sim \\mathcal N(\\mu,\\sigma^2).$\n", "\n", "![image.png](./images/normal4.png)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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0Z+DzZvZdM+uqsZhZg5l9j9BE9udY+QOBhVn28zah+S1bMppKaLZr62twUXPh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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = logspace(-9,1,1001)+1e-9\n", "showDistribution(stats.lognorm(2), '',\n", " 'Lognormal Distribution', 'X', 'lognorm(X)','', xmin=-0.1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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/ZDx3VZ1Qi7hMjJu5dg+b9x3h7jE9vA6l3kpvkszJPVvzxoIt/OKUbiQl2O1L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\nr6Rjy0b87Ggb08yElohwz+k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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The log-lin plot has to be done by hand:\n", "plot(log(x), stats.lognorm.pdf(x,2))\n", "xlim(-10, 4)\n", "title('Lognormal Distribution')\n", "xlabel('log(X)')\n", "ylabel('lognorm(X)')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Binomial Distribution\n", "\n", "The probability of getting exactly $k$ successes in $n$ independent Bernoulli trials is given by the probability density function:\n", "\n", "$$f(k,n,p) = \\Pr(k;n,p) = \\Pr(X = k) = \\binom{n}{k}p^k(1-p)^{n-k}$$\n", "\n", "for k  = 0, 1, 2, ...,  n, where $\\binom{n}{k} =\\frac{n!}{k!(n-k)!}$ is the **binomial coefficient**\n", "\n", "- $k$ successes occur with probability pk\n", "- $n-k$ failures occur with probability (1 − p)n − k. \n", "\n" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T11:47:32.475585Z", "start_time": "2020-05-08T11:47:32.318557Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "bd1 = stats.binom(20, 0.5)\n", "bd2 = stats.binom(20, 0.7)\n", "bd3 = stats.binom(40, 0.5)\n", "k = arange(40)\n", "plot(k, bd1.pmf(k), 'o-b')\n", "plot(k, bd2.pmf(k), 'd-r')\n", "plot(k, bd3.pmf(k), 's-g')\n", "title('Binomial distribition')\n", "legend(['p=0.5 and n=20', 'p=0.7 and n=20', 'p=0.5 and n=40'])\n", "xlabel('X')\n", "ylabel('P(X)');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Poisson Distribution\n", "\n", "The Poisson distribution is popular for modeling the number of times an event occurs in an interval of time or space.\n", "\n", "A discrete **random variable** X is said to have a P$oisson distribution with parameter λ > 0, if, for k = 0, 1, 2, ..., the **probability mass function** of X is given by:\n", "\n", "$$\\!f(k; \\lambda)= \\Pr(X = k)= \\frac{\\lambda^k e^{-\\lambda}}{k!},$$\n", "\n", "The positive **real number** λ is equal to the **expected value** of X and also to its **variance**\n", "\n", "$$\\lambda=\\operatorname{E}(X)=\\operatorname{Var}(X).$$\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "ExecuteTime": { "end_time": "2020-05-08T12:04:12.315789Z", "start_time": "2020-05-08T12:04:12.141989Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pd = stats.poisson(1)\n", "pd4 = stats.poisson(4)\n", "pd10 = stats.poisson(10)\n", "plot(k, pd.pmf(k),'x-', label = '1')\n", "plot(k, pd4.pmf(k),'x-', label = '4')\n", "plot(k, pd10.pmf(k),'x-', label = '10')\n", "title('Poisson distribition')\n", "xlabel('X')\n", "ylabel('P(X)')\n", "legend();" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "![image.png](./images/end.png)" ] } ], "metadata": { "celltoolbar": "Slideshow", "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": "3.7.6" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 1 }