HalfNormalDistribution

The half-normal distribution with parameter $\theta$ — $\sqrt{\pi/2}\,|Z|/\theta$ for a standard normal $Z$ .

HalfNormalDistribution(theta)an inert distribution object — carries

\theta

, unevaluated. Wolfram's own parameterization:

\theta

is inversely proportional to scale, not the scale itself.

Typed signatures

Type	Package	Applies
`(real<0..>) -> distribution`	`statistics`	always

Domain: Statistics

Details

$PDF(x) = \frac{2\theta}{\pi}\, e^{-x^2\theta^2/\pi}$ for $x \geq 0$ .
$CDF(x) = Erf(x\theta/\sqrt{\pi})$ via Erf, clamped to $0$ below $x=0$ .
$Mean = 1/\theta$ , $Variance = (\pi-2)/(2\theta^2)$ , both exact.
RandomVariate samples $\sqrt{\pi/2}\,|Z|/\theta$ for a standard normal $Z$ .
$\theta=\sqrt{\pi/2}$ is the standard half-normal $|Z|$ , the norm of one standard normal.