\begin{definition}[Definition:Erlang Distribution]
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 $\lambda$ {{iff}} 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: 
:$X \sim \map {\operatorname {Erlang} } {k, \lambda}$
\end{definition}