Image:Cauchy distribution cdf.png

Cumulative distribution function for the Cauchy distribution

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gnuplot source under GPL:

dcauchy(x,l,s) = 1.0 / (pi * s * (1 + ((x-l)*1.0/s)**2))
pcauchy(x,l,s) = 0.5 + atan((x-l)*1.0/s) / pi
qcauchy(p,l,s) = l - s * 1.0/tan(pi * p)

set samples 1001
set terminal postscript enhanced color solid lw 2 "Times-Roman" 20
set output

set xtics 1
set ytics 0.1

#f(x,y,z) = dcauchy(x,y,z)
#set key 3.6,0.65

f(x,y,z) = pcauchy(x,y,z)
set key 3.6,0.2

plot [-5:5] \
    f(x,  0, 0.5) title "{/Times-Italic x}_0 =  0, {/Symbol g} = 0.5", \
    f(x,  0, 1)   title "{/Times-Italic x}_0 =  0, {/Symbol g} = 1.0", \
    f(x,  0, 2)   title "{/Times-Italic x}_0 =  0, {/Symbol g} = 2.0", \
    f(x, -2, 1)   title "{/Times-Italic x}_0 = -2, {/Symbol g} = 1.0"

This work is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This work is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. العربية | Česky | Deutsch | English | Español | فارسی | Français | Italiano | 日本語 | Nederlands | Polski | Português | Русский | Svenska | Türkçe | 简体中文 | 正體中文 | +/-