Summary
Description  The probability density function of Gamma distribution for different parameters. See below for the spec and Gnuplot source code. 
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Spec and Gnuplot Source Code
For the readers who are interested in Erlang distribution, we have prepared another specific image (see right). Note that in Erlang distribution the shape parameter k must take integers.
Originally, the pdf of Gamma distribution is
Let α = k, and β = 1/θ. Then
Hence
which directly gives the code below.
# Author: Autopilot, Ika # Date: 12/08/2014 set term svg size 800,600 font 'Times, 24' enhanced set output 'gamma_dist_pdf.svg' set samples 1001 set xtics 0,2 set ytics 0,0.1 set mxtics 10 set mytics 10 set yrange [0:0.5] set key top right Left reverse # Ln f(x; k, theta) # Commonly, we denote a = alpha = k and b = beta = 1/theta. ln_f(x, a, b) = a*log(b)  lgamma(a) + (a1)*log(x)  b*x # f(x; k, theta) f(x, k, theta) = (x<0)? 0 : (x==0)? ((k<1)? 1/0 : (k==1)? theta : 0)\ : (theta==0)? 0 : exp(ln_f(x, k, 1.0/theta)) plot [0:20] \ f(x, 1.0, 2.0) t "k = 1.0, {/Symbol q} = 2.0" lw 2 lc rgb "red", \ f(x, 2.0, 2.0) t "k = 2.0, {/Symbol q} = 2.0" lw 2 lc rgb "orange", \ f(x, 3.0, 2.0) t "k = 3.0, {/Symbol q} = 2.0" lw 2 lc rgb "yellow", \ f(x, 5.0, 1.0) t "k = 5.0, {/Symbol q} = 1.0" lw 2 lc rgb "green", \ f(x, 9.0, 0.5) t "k = 9.0, {/Symbol q} = 0.5" lw 2 lc rgb "black", \ f(x, 7.5, 1.0) t "k = 7.5, {/Symbol q} = 1.0" lw 2 lc rgb "blue", \ f(x, 0.5, 1.0) t "k = 0.5, {/Symbol q} = 1.0" lw 2 lc rgb "purple" set term x11 set output
This is a retouched picture, which means that it has been digitally altered from its original version. Modifications: Recreated as svg with gnuplot. The original can be viewed here: Gamma distribution pdf.png. Modifications made by Autopilot.

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 File:Gamma_distribution_pdf.png licensed with Ccbysa3.0migrated, GFDL, GPL
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