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File:Gamma distribution pdf.svg

From Wikipedia, the free encyclopedia

Summary

Description The probability density function of Gamma distribution for different parameters. See below for the spec and Gnuplot source code.
Date (UTC)
Source
Author

Spec and Gnuplot Source Code

Erlang dist pdf.svg

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.

Lissajous small.svg
This W3C-unspecified plot was created with Gnuplot.
# 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) + (a-1)*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


Applications-graphics.svg
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.

I, the copyright holder of this work, hereby publish it under the following licenses:
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Original upload log

This image is a derivative work of the following images:

  • File:Gamma_distribution_pdf.png licensed with Cc-by-sa-3.0-migrated, GFDL, GPL
    • 2005-03-10T20:34:05Z MarkSweep 1300x975 (162472 Bytes) new version of PDF and matching CDF
    • 2005-03-10T17:45:44Z Cburnett 960x720 (138413 Bytes) Probability density function for the Gamma distribution {{GFDL}}

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