Hyper Erlang distribution

In probability theory, a hyper-Erlang distribution is a continuous probability distribution which takes a particular Erlang distribution E_i with probability p_i. A hyper-Erlang distributed random variable X has probability density function given by

where each p_i > 0 with the p_i summing to 1 and each of the E_li being an Erlang distribution with l_i stages each of which has parameter λ_i.