In probability theory, a hyper-Erlang distribution is a continuous probability distribution which takes a particular Erlang distribution E<sub>i</sub> with probability p<sub>i</sub>. A hyper-Erlang distributed random variable X has a probability density function given by
where each p<sub>i</sub> > 0 with the p<sub>i</sub> summing to 1 and each of the E<sub>l<sub>i</sub></sub> being an Erlang distribution with l<sub>i</sub> stages each of which has parameter û<sub>i</sub>.