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Probability density function for the Gamma distribution
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no FrontCover Texts, and no BackCover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue 
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gnuplot source under GPL:
_ln_dgamma(x, a, b) = a*log(b)  lgamma(a) + (a1)*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 "TimesRoman" 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 "{/TimesItalic k} = 1, {/Symbol q} = 2.0", \ f(x,2,2.0) title "{/TimesItalic k} = 2, {/Symbol q} = 2.0", \ f(x,3,2.0) title "{/TimesItalic k} = 3, {/Symbol q} = 2.0", \ f(x,5,1.0) title "{/TimesItalic k} = 5, {/Symbol q} = 1.0", \ f(x,9,0.5) title "{/TimesItalic k} = 9, {/Symbol q} = 0.5" lt 7

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