Summary edit

DescriptionErlang dist pdf.svg	English: The probability density function of Erlang distribution.
Date	8 December 2014
Source	Own work
Author	IkamusumeFan
Other versions

Gnuplot Source Code edit

 

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 'erlang_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, mu)
# Commonly, we denote a = alpha = k and b = beta = 1/mu.
ln_f(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x

# f(x; k, mu)
f(x, k, mu) = (x<0)? 0 : (x==0)? ((k<1)? 1/0 : (k==1)? mu : 0)\
 : (mu==0)? 0 : exp(ln_f(x, k, 1.0/mu))

plot [0:20] \
    f(x, 1.0, 2.0) t "k = 1, {/Symbol m} = 2.0" lw 2 lc rgb "red", \
    f(x, 2.0, 2.0) t "k = 2, {/Symbol m} = 2.0" lw 2 lc rgb "orange", \
    f(x, 3.0, 2.0) t "k = 3, {/Symbol m} = 2.0" lw 2 lc rgb "yellow", \
    f(x, 5.0, 1.0) t "k = 5, {/Symbol m} = 1.0" lw 2 lc rgb "green", \
    f(x, 7.0, 0.5) t "k = 7, {/Symbol m} = 0.5" lw 2 lc rgb "black", \
	f(x, 9.0, 1.0) t "k = 9, {/Symbol m} = 1.0" lw 2 lc rgb "blue", \
	f(x, 1.0, 1.0) t "k = 1, {/Symbol m} = 1.0" lw 2 lc rgb "purple"

set term x11
set output

Licensing edit

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• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue