Erlang Distribution

 Erlang Distribution

The Erlang Distribution is a continuous distribution which is a special distribution of the Gamma distribution.

PDF

The continuous random variable X is said to have an erlang distribution with a scale parameter of $\theta >0$ and the parameter $r$, namely $X\sim Erl(\theta,r)$.

so

$f(x)=\frac{1}{\theta^{r}(r-1)}x^{r-1}e^{-\frac{x}{\theta}} \hspace{1cm};x>0$

where r is a positive integer.

Mean

Varians

CDF

MGF