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Cumulative distribution function for the Cauchy distribution
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"
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