File:Gamma distribution pdf.svg
Original file (SVG file, nominally 800 × 600 pixels, file size: 115 KB)
Captions
Summary
[edit]DescriptionGamma distribution pdf.svg | 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
[edit]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.
# 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
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.
|
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
| ||
This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
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 Front-Cover Texts, and no Back-Cover 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 |
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.http://www.gnu.org/licenses/gpl.htmlGPLGNU General Public Licensetruetrue |
Original upload log
[edit]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
Uploaded with derivativeFX
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 23:05, 8 December 2014 | 800 × 600 (115 KB) | IkamusumeFan (talk | contribs) | Change curve colors for better display. | |
22:50, 8 December 2014 | 800 × 600 (115 KB) | IkamusumeFan (talk | contribs) | Enlarge the font sizes for better display in the article. Add two more lines when the shape parameter does not take integers. | ||
20:57, 18 August 2014 | 800 × 600 (77 KB) | Svjo (talk | contribs) | Reverted to version as of 18:32, 26 June 2010 | ||
20:56, 18 August 2014 | 802 × 625 (65 KB) | Svjo (talk | contribs) | font sizes | ||
18:32, 26 June 2010 | 800 × 600 (77 KB) | Autopilot (talk | contribs) | {{Information |Description=<pre> _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 |
You cannot overwrite this file.
File usage on Commons
The following 2 pages use this file:
File usage on other wikis
The following other wikis use this file:
- Usage on ar.wikipedia.org
- Usage on be.wikipedia.org
- Usage on ca.wikipedia.org
- Usage on en.wikipedia.org
- Usage on en.wikibooks.org
- Usage on es.wikipedia.org
- Usage on fi.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on gl.wikipedia.org
- Usage on it.wikipedia.org
- Usage on ja.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on sv.wikipedia.org
- Usage on tr.wikipedia.org
- Usage on uk.wikipedia.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Short title | Gnuplot |
---|---|
Image title | Produced by GNUPLOT 4.6 patchlevel 3 |
Width | 800 |
Height | 600 |