File:Gamma distribution pdf.png

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Probability density function for the Gamma distribution

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gnuplot source under GPL:

_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x
dgamma(x, shape, rate) =\
 (x<0)? 0 :\
 (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) :\
 (rate==0)? 0 :\
 exp(_ln_dgamma(x, shape, rate))
pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)

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

set xtics 0,2
set ytics 0,0.1

f(x, k, t) = dgamma(x, k, 1.0/t)
set key top right

#f(x, k, t) = pgamma(x, k, 1.0/t)
#set key bottom right

plot [0:20] \
    f(x,1,2.0) title "{/Times-Italic k} = 1, {/Symbol q} = 2.0", \
    f(x,2,2.0) title "{/Times-Italic k} = 2, {/Symbol q} = 2.0", \
    f(x,3,2.0) title "{/Times-Italic k} = 3, {/Symbol q} = 2.0", \
    f(x,5,1.0) title "{/Times-Italic k} = 5, {/Symbol q} = 1.0", \
    f(x,9,0.5) title "{/Times-Italic k} = 9, {/Symbol q} = 0.5" lt 7

This vector image was created with gnuplot.

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 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 version 2 and version 3 of the GNU General Public License for more details.

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