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Summary

Description Cumulative distribution function for the Gamma distribution. Related links: *w:Gamma distribution *Image:Gamma distribution pdf.png
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Spec and Gnuplot Source Code

For the readers who may be interested in Erlang distribution, please see its cdf on the right. Note that Erlang is a proper subset of Gamma, since its shape parameter only admits integers.

 
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_cdf.svg'
set samples 1001

set xtics 0,2
set ytics 0,0.1
set mxtics 10
set mytics 10
set yrange [0:1.0]
set key bottom right

# F(x; k, theta)
F(x, k, theta) = (x<0)? 0 : igamma(k, x/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 cdf.png. Modifications made by Autopilot.

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Original upload log

This image is a derivative work of the following images:

  • File:Gamma_distribution_cdf.png licensed with Cc-by-sa-3.0-migrated, GFDL, GPL
    • 2005-03-10T20:34:08Z MarkSweep 1300x975 (178972 Bytes) new version of CDF and matching PDF
    • 2005-03-10T20:18:04Z Cburnett 960x720 (146011 Bytes) Cumulative distribution function for the Gamma distribution {{GFDL}}
    • 2005-03-10T17:46:02Z Cburnett 960x720 (129377 Bytes) Cumulative distribution function for the Gamma distribution {{GFDL}}

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26 June 2010

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Date/TimeThumbnailDimensionsUserComment
current23:08, 8 December 2014Thumbnail for version as of 23:08, 8 December 2014800 × 600 (115 KB)IkamusumeFanEnlarge font sizes; Give two more curves to address the cases in which the shape parameter does not take integers.
18:37, 26 June 2010Thumbnail for version as of 18:37, 26 June 2010800 × 600 (76 KB)Autopilot{{Information |Description=Related links: *w:Gamma distribution *Image:Gamma distribution pdf.png Cumulative distribution function for the Gamma distribution <pre> _ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x dgamma(x, shape,

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