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Probability density function for the Beta distribution

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gnuplot source under GPL:

dbeta(x,a,b) = exp((a-1)*log(x)+(b-1)*log(1-x)-lgamma(a)-lgamma(b)+lgamma(a+b))
pbeta(x,a,b) = ibeta(a,b,x)

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

set xrange [0:1]
set xtics 0.1

f(x,y,z) = dbeta(x,y,z)
set yrange [0:2.6]
set ytics 0.2
set key 0.61,2.4

#f(x,y,z) = pbeta(x,y,z)
#set ytics 0.1
#set key 0.21,0.94

plot \
    f(x, 0.5,0.5) title "{/Symbol a} = {/Symbol b} = 0.5", \
    f(x, 5,  1)   title "{/Symbol a} = 5, {/Symbol b} = 1", \
    f(x, 1,  3)   title "{/Symbol a} = 1, {/Symbol b} = 3", \
    f(x, 2,  2)   title "{/Symbol a} = 2, {/Symbol b} = 2", \
    f(x, 2,  5)   title "{/Symbol a} = 2, {/Symbol b} = 5" lt 7
GNU head 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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