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

 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

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