File:Folded normal pdf.svg

Probability density function (pdf) of a folded-normal random variable with ${\displaystyle \mu =1}$, ${\displaystyle \sigma =1}$. The graph is generated using gnuplot:

set terminal svg enhanced size 640 360
set samples 1001  # high quality
set border 31 linewidth .3 # thin border
set output "folded_normal.svg"

set notitle
set xrange [-3:5]
set ytics 0.1

sigma=1.0
mu=1.0
n(x)=1.0/(sqrt(2.0*pi)*sigma) * exp( -(mu-x)**2/(2.0*sigma**2) )
nreflect(x)= (x<0) ? 1/0 : n(-x)
fn(x)= (x<-0.01) ? 0 : (x<0) ? 1/0 : (n(x) + n(-x)) 

set arrow 1 from  0,0 to  0,0.5 nohead lt 0

plot	n(x) title "normal density",\
	fn(x) title "folded-normal density" lw 3,\
	nreflect(x) notitle with l lt 0

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.