Hyper-Erlang distribution

{{Short description|Continuous probability distribution}}

File:Hyper-Erlang distribution.svg

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

:$A(x)\; =\; \backslash sum\_\{i=1\}^n\; p\_i\; E\_\{l\_i\}(x)$

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.{{Cite book | doi = 10.1515/9783110936025.61 | chapter = 2. Defining parameters of queueing systems | title = Queueing Theory | last1 = Bocharov | first1 = P. P.| last2 = D'Apice | first2 =C.| last3 = Pechinkin | first3 = A. V.| year = 2003 | isbn = 9783110936025 }}{{Cite journal | last1 = Yuguang Fang | last2 = Chlamtac | first2 = I. | doi = 10.1109/26.774856 | title = Teletraffic analysis and mobility modeling of PCS networks | journal = IEEE Transactions on Communications| volume = 47 | issue = 7 | pages = 1062 | year = 1999 | doi-access = free }}{{Cite journal | last1 = Fang | first1 = Y. | journal = Wireless Networks | title = Hyper-Erlang Distribution Model and its Application in Wireless Mobile Networks| volume = 7 | issue = 3 | pages = 211–219 | doi = 10.1023/A:1016617904269 | year = 2001 | publisher = Kluwer Academic Publishers}}