File:Cauchy distribution pdf.png

Summary

Probability density 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 colour 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" 

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