MaxwellDistribution

The Maxwell(-Boltzmann) distribution with scale $\sigma$ — $\sigma$ times a ChiDistribution( $3$ ) draw.

MaxwellDistribution(sigma)an inert distribution object — carries

\sigma

, unevaluated.

Typed signatures

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

Domain: Statistics

Details

$PDF(x) = \sqrt{2/\pi}\,x^2 e^{-x^2/(2\sigma^2)}/\sigma^3$ for $x \geq 0$ .
$CDF(x) = P(3/2, x^2/(2\sigma^2))$ via GammaRegularized (the standard chi-square-CDF identity for Maxwell), clamped to $0$ below $x=0$ .
$Mean = 2\sigma\sqrt{2/\pi}$ , $Variance = \sigma^2(3\pi-8)/\pi$ , both exact.
RandomVariate samples $\sigma\sqrt{V}$ for an independent ChiSquareDistribution( $3$ ) draw $V$ .