Editing Erlang distribution (section)

=== Probability density function ===

The [[probability density function]] of the Erlang distribution is

:<math>f(x; k,\lambda)={\lambda^k x^{k-1} e^{-\lambda x} \over (k-1)!}\quad\mbox{for }x, \lambda \geq 0,</math>

The parameter ''k'' is called the shape parameter, and the parameter <math>\lambda</math> is called the rate parameter.

An alternative, but equivalent, parametrization uses the scale parameter <math>\beta</math>, which is the reciprocal of the rate parameter (i.e., <math>\beta = 1/\lambda</math>):

:<math>f(x; k,\beta)=\frac{ x^{k-1} e^{-\frac{x}{\beta}} }{\beta^k (k-1)!}\quad\mbox{for }x, \beta \geq 0.</math>

When the scale parameter <math>\beta</math> equals 2, the distribution simplifies to the [[chi-squared distribution]] with 2''k'' degrees of freedom. It can therefore be regarded as a [[generalized chi-squared distribution]] for even numbers of degrees of freedom.