{ "cells": [ { "cell_type": "markdown", "id": "7f5be4f6-498f-45a3-a97f-a3617a73bfe5", "metadata": {}, "source": [ "# T distribution" ] }, { "cell_type": "markdown", "id": "4ce5ed6c-d5dd-418f-942c-1eb3602c366d", "metadata": {}, "source": [ "Let's investigate how shape of the t distribution curve look likes." ] }, { "cell_type": "code", "execution_count": 1, "id": "c8cc4961-b6b2-4a1a-baf7-89a09b29f272", "metadata": {}, "outputs": [], "source": [ "# import required libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats\n", "from IPython.display import display" ] }, { "cell_type": "markdown", "id": "80f36bec-c0af-4d41-8c1b-34dd40d860ba", "metadata": {}, "source": [ "Let's now investigate how shape of the t distribution curve changes with respect to degrees of freedom ($\\nu$). We will define a function first to simplify our calculations." ] }, { "cell_type": "code", "execution_count": 2, "id": "119b598b-baf0-4f33-a116-ade95cc03ae0", "metadata": {}, "outputs": [], "source": [ "# define a Python function with three parameters\n", "\n", "def t_dist_curve(dof, ltype, col):\n", " \n", " fig, ax = plt.subplots(figsize = (6, 6))\n", " \n", " #use zip for parallel iteration\n", " for d, l, cl in zip(dof, ltype, col):\n", " #generate 10000 random variables for given degrees of freedom\n", " x = stats.t.rvs(df = d, size = 10000)\n", " x1 = np.sort(x)\n", " plt.plot(x1, stats.t.pdf(x1, df = d), \n", " ls = l, c = cl, label = r'$\\nu=%.1f$' % (d)) \n", " \n", " plt.xlim(-15, 15)\n", " plt.ylim(0, 0.4)\n", " plt.xlabel('$x$')\n", " plt.ylabel(r'$f(x|\\nu)$')\n", " plt.title('T distribution curve')\n", " plt.legend(loc='upper right')\n", " plt.show()" ] }, { "cell_type": "markdown", "id": "dd15f1f5-1506-4b18-8f1b-34c62c9ae2f3", "metadata": {}, "source": [ "Now play with the function to see the changes on the normal distribution curve." ] }, { "cell_type": "code", "execution_count": 4, "id": "c31a6b1e-d89d-4dcd-9450-5d3e550ce7df", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "None" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## change the following values as you wish\n", "## define the input arguments (values of the parameters)\n", "dof_values = [2, 5, 10, 30]\n", "linestyles = ['-', '--', '-.', ':']\n", "colors = ['blue', 'green','red','black']\n", "\n", "t_curve = t_dist_curve(dof = dof_values, ltype = linestyles, col = colors)\n", "\n", "display(t_curve)" ] }, { "cell_type": "markdown", "id": "01aa9ad5-d8d2-409e-b89a-dec3009b680f", "metadata": {}, "source": [ "Compare the standard normal distribution cuver with t distribution curver with df = 30." ] }, { "cell_type": "code", "execution_count": 23, "id": "ca9119a2-209f-443e-8bca-37c3a03e3df4", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize = (7, 7))\n", " \n", " \n", "plt.subplot(2, 1, 1) \n", "d1 = 5\n", "#generate 10000 random variables for given degrees of freedom\n", "x1 = stats.t.rvs(df = d1, size = 10000)\n", "x1 = np.sort(x1)\n", "plt.plot(x1, stats.t.pdf(x1, df = d1), c ='black', label = r'T dist. with $\\nu=%.1f$' % (d1)) \n", " \n", "mu = 0\n", "sigma = 1\n", "x3 = stats.norm.rvs(loc = mu, scale = sigma, size = 10000)\n", "x3 = np.sort(x3)\n", " \n", "plt.plot(x3, stats.norm.pdf(x3, loc = mu, scale = sigma), c ='red', label = r'Normal distribution with $\\mu=%.1f,\\sigma^2=%.1f$' % (mu, sigma*sigma))\n", "plt.ylim(0, 0.5)\n", "plt.ylim(0, 0.45)\n", "plt.xlim(-10, 10)\n", "plt.xlabel('$x$')\n", "plt.ylabel('Density')\n", "plt.legend(loc='upper right')\n", "\n", "\n", "plt.subplot(2, 1, 2) \n", "d2 = 30\n", "#generate 10000 random variables for given degrees of freedom\n", "x2 = stats.t.rvs(df = d2, size = 10000)\n", "x2 = np.sort(x2)\n", "plt.plot(x2, stats.t.pdf(x2, df = d2), c ='black', label = r'T dist. with $\\nu=%.1f$' % (d2)) \n", "plt.plot(x3, stats.norm.pdf(x3, loc = mu, scale = sigma), c ='red', label = r'Normal distribution with $\\mu=%.1f,\\sigma^2=%.1f$' % (mu, sigma*sigma))\n", "plt.ylim(0, 0.5)\n", "plt.xlim(-10, 10)\n", "plt.xlabel('$x$')\n", "plt.ylabel('Density')\n", "plt.legend(loc='upper right')\n", "\n", "plt.title('Comparison of t dist. with standard normal dist. curve')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1fc863a6-0d8f-45aa-878a-5196d98e261b", "metadata": {}, "source": [ "Calculate probabilities associated with t distribution with 'stats.t.cdf(x, df)'." ] }, { "cell_type": "code", "execution_count": 17, "id": "e8dbacc2-8c6d-47af-bd6b-dd200241511c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.02500588590855568" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1-stats.t.cdf(2.228, df = 10)" ] }, { "cell_type": "markdown", "id": "60501abb-9fec-4dfb-baac-c441900773fd", "metadata": {}, "source": [ "https://en.wikipedia.org/wiki/Student%27s_t-distribution" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.12" } }, "nbformat": 4, "nbformat_minor": 5 }