ErlangDistribution

The Erlang distribution with shape $n$ and rate $\lambda$ — $GammaDistribution(n, 1/\lambda)$ under the hood.

ErlangDistribution(n, lambda)an inert distribution object — carries

n, \lambda

, unevaluated.

Typed signatures

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

Domain: Statistics

Details

$PDF(x) = \lambda^n x^{n-1}e^{-\lambda x}/\Gamma(n)$ for $x \geq 0$ .
$CDF(x) = P(n, \lambda x)$ , the regularized lower incomplete gamma via GammaRegularized (same upper-tail-native convention as ChiSquareDistribution), clamped to $0$ below $x=0$ .
$Mean = n/\lambda$ , $Variance = n/\lambda^2$ , both exact.
RandomVariate samples via the same Marsaglia–Tsang GammaDistribution draw, shape $n$ , scale $1/\lambda$ .