ChiSquareDistribution

The chi-square distribution with $k$ degrees of freedom — $GammaDistribution(k/2, 2)$ under the hood.

ChiSquareDistribution(k)an inert distribution object — carries

k

, unevaluated.

Typed signatures

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

Domain: Statistics

Details

$PDF(x) = x^{k/2-1} e^{-x/2} / (2^{k/2}\Gamma(k/2))$ for $x \geq 0$ — no domain clamp on the PDF itself (same policy as GammaDistribution).
$CDF(x) = P(k/2, x/2)$ , the regularized lower incomplete gamma, via GammaRegularized (compute-engine's native two-argument form is the upper tail), clamped to $0$ below $x=0$ .
$Mean = k$ , $Variance = 2k$ , both exact.
RandomVariate samples via the same Marsaglia–Tsang GammaDistribution draw, shape $k/2$ , scale $2$ .