{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "# Table of Contents\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "from scipy import stats\n", "from matplotlib import pyplot as pl\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Typová rozdělení\n", "===================\n", "\n", "Diskrétní\n", "--------------------\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Binomické\n", "\n", "výsledky opakovaných pokusů s náhodným jevem, který má 2 možné výsledky\n", "\n", "\\begin{equation} \\pi_n(r)= \\frac{n!}{p! (n-p)!} p^r (1-p)^{n-r} \\end{equation}\n", "\n", "__střední hodnota__ : $np$ \n", "__disperze__ : $np(1-p)$ \n", "__asymetrie__ : $\\frac{1-2p}{\\sqrt{np(1-p)}}$ \n", "__excess__ : $\\frac{1-6p(1-p)}{np(1-p)}$ \n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Poissonovo\n", "\n", "\\begin{equation} \\pi_n(r)= \\frac{1}{r!} \\mu^r \\mathrm{e}^{-\\mu} \\label{eq:pois} \\end{equation}\n", "\n", "__střední hodnota__ : $\\mu$ \n", "__disperze__ : $\\mu$ \n", "__asymetrie__ : $1/\\sqrt{\\mu}$ \n", "__excess__ : $1/\\mu$ \n", "\n", "limitně pro $\\mu \\to \\infty$ se blíží $N(\\mu,\\sqrt{\\mu})$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Spojité\n", "-----------------\n" ] }, { "cell_type": "markdown", "metadata": { "subvar": 1.23 }, "source": [ "### rovnoměrné rozdělení\n", "\n", "$$ f(x)=1/(b-a)\\ \\ldots\\ x \\in < a,b >$$\n", "\n", "__střední hodnota__ : $(a+b)/2$ \n", "__disperze__ : $(a-b)^2/12$ \n", "__asymetrie__ : 0 \n", "__excess__ : $-1.2$ \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### exponenciální rozdělení\n", "\n", "$$ f(x)=\\exp(\\frac{-x}{\\mu})/\\mu $$\n", "\n", "__střední hodnota__ : $\\mu$ \n", "__disperze__ : $\\mu^2$ \n", "__asymetrie__ : 2 \n", "__excess__ : 6 \n", "\n", "charakter. funkce $1/(1-\\i\\mu t)$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Breit-Wigner (Cauchy, Lorentz)\n", "\n", "$$ f(x)=\\frac{1}{\\pi} \\frac{1}{1+(x-\\mu)^2} $$\n", "\n", "__střední hodnota__ : nedef. () \n", "__disperze__ : $\\infty$ \n", "\n", "charakter. funkce $\\exp^{-|t|}$\n", "\n", "*generování*: $\\tan \\pi(r-1/2)$ pro *r* s rovnom. rozdělením v (0,1)\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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D/v36ebLLl6fej/+w3od4ZfDi681f2zQeM48dmD8/a0lxd4ARW0aQwSMDHzdI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\nDOGLTV+w6/wu/tf4f7xd421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