Image:Gamma distribution pdf.png
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See the image on the commons for gnuplot source.
Related links:
- Gamma distribution
- Image:Gamma distribution pdf.png
- Image:Gamma distribution cdf.png
_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,1,1.0) title "{/Times-Italic k} = 1, {/Symbol q} = 1.0", \
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
Probability density function for the Gamma distribution
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
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