Probability density function (pdf) of a folded-normal random variable with , .
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
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