Hyper-Erlang distribution

In probability theory, a hyper-Erlang distribution is a continuous probability distribution which takes a particular Erlang distribution Ei with probability pi. A hyper-Erlang distributed random variable X has a probability density function given by
 * $$ A(x) = \sum_{i=1}^n p_i E_{l_i}(x)$$

where each pi > 0 with the pi summing to 1 and each of the El i being an Erlang distribution with li stages each of which has parameter λi.