Definition:Erlang Distribution

Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $\Img X = \hointr 0 \infty$.

Let $k$ be a strictly positive integer.

Let $\lambda$ be a strictly positive real number.

$X$ is said to have an Erlang distribution with parameters $k$ and $\lambda$ it has probability density function:


 * $\map {f_X} x = \dfrac {\lambda^k x^{k - 1} e^{- \lambda x} } {\map \Gamma k}$

where $\Gamma$ denotes the gamma function.

This is written:


 * $X \sim \map {\operatorname {Erlang} } {k, \lambda}$