{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import math\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm\n", "from scipy.special import erf\n", "from scipy.stats import chi2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Error function and cumulative of the gaussian\n", "### $erf(x) = \\frac{1}{2\\pi} \\int_0^x e^{-t^2}dt$\n", "Cumulative of \"unit\" gaussian $G(\\mu=0, \\sigma=1)$ is $0.5(1+errf(x))$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Error function is erf(x) = (1/2pi)*Integral_from_0_to_x of e^{-t^2}dt\n", "# The cumulative of the 'unit' gaussian is = 0.5 * (1+erf(x)) \n", "x = np. linspace(-3,3,2000)\n", "ax = plt.subplot(111)\n", "ax.plot(x, 0.5*(1+erf(x)))\n", "ax.grid()\n", "ax.set_xlabel(\"$\\sigma$ from mean\")\n", "_ = ax.set_ylim(bottom=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "---\n", "\n", "### $\\chi^2 = \\sum_i^N \\frac{(x_i-\\mu_i)^2}{\\sigma_i^2}$\n", "Number of degrees of freedom = $n = N$
\n", "or $n = N-p$ if $\\mu_i$ are fit to $p$ parameters
\n", "If $x_i$ are $G(\\mu_i, \\sigma_i)$ then $\\chi^2$ follows this distribution\n", "### $f(x) dx = \\frac{1}{\\Gamma(n/2)} x^{n/2-1} e^{-n/2}$\n", "The expectation value (mean) is $<\\chi^2> = n$
\n", "$\\chi^2/n \\approx 1$ is a rule-of-thumb for a good fit
\n", "But it there is much more to it in the tails." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot chisquare per ndof for different ndof\n", "ndof = [1,2,4,8,15,20]\n", "x = np. linspace(0,5,1000)\n", "figure = plt.figure(figsize=(10, 4.5))\n", "ax = plt.subplot(1,2,1)\n", "for n in ndof:\n", " ax.plot(x, chi2.pdf(n*x, df=n), label=\"ndof =\"+str(n))\n", "ax.grid()\n", "ax.set_ylim(0.,0.5)\n", "ax.legend()\n", "ax.set_xlabel(\"$\\chi^2$/ndof\")\n", "ax.set_xlim(x[0],x[-1])\n", "\n", "ax = plt.subplot(1,2,2)\n", "for n in ndof:\n", " ax.plot(x, chi2.pdf(n*x, df=n), label=\"ndof =\"+str(n))\n", "ax.grid()\n", "ax.legend()\n", "ax.set_xlabel(\"$\\chi^2$/ndof\")\n", "ax.set_yscale('log')\n", "ax.set_ylim(1e-6,1)\n", "_ = ax.set_xlim(x[0],x[-1])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }