Hyper-Erlang distribution explained

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 a probability density function given by

A(x) = \sum ^{n} _{i =1} p _{i} E _{l _{i}} (x) 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.^{[1] [2] [3]}

See also

• Phase-type distribution

Notes and References

1. Book: 10.1515/9783110936025.61 . 2. Defining parameters of queueing systems . Queueing Theory . Bocharov . P. P.. D'Apice . C.. Pechinkin . A. V.. 2003 . 9783110936025 .
2. Yuguang Fang . Chlamtac . I. . 10.1109/26.774856 . Teletraffic analysis and mobility modeling of PCS networks . IEEE Transactions on Communications. 47 . 7 . 1062 . 1999 . free .
3. Fang . Y. . Wireless Networks . Hyper-Erlang Distribution Model and its Application in Wireless Mobile Networks. 7 . 3 . 211–219 . 10.1023/A:1016617904269 . 2001 . Kluwer Academic Publishers.