Hyper-Erlang distribution
Continuous probability 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
where each pi > 0 with the pi summing to 1 and each of the Eli being an Erlang distribution with li stages each of which has parameter λi.[1][2][3]
See also
- Phase-type distribution
References
- ^ Bocharov, P. P.; D'Apice, C.; Pechinkin, A. V. (2003). "2. Defining parameters of queueing systems". Queueing Theory. doi:10.1515/9783110936025.61. ISBN 9783110936025.
- ^ Yuguang Fang; Chlamtac, I. (1999). "Teletraffic analysis and mobility modeling of PCS networks". IEEE Transactions on Communications. 47 (7): 1062. doi:10.1109/26.774856.
- ^ Fang, Y. (2001). "Hyper-Erlang Distribution Model and its Application in Wireless Mobile Networks". Wireless Networks. 7 (3). Kluwer Academic Publishers: 211–219. doi:10.1023/A:1016617904269.
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Probability distributions (list)
univariate
with finite support |
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with infinite support |
univariate
univariate
continuous- discrete |
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(joint)
- Discrete:
- Ewens
- multinomial
- Continuous:
- Dirichlet
- multivariate Laplace
- multivariate normal
- multivariate stable
- multivariate t
- normal-gamma
- Matrix-valued:
- LKJ
- matrix normal
- matrix t
- matrix gamma
- Wishart
- Univariate (circular) directional
- Circular uniform
- univariate von Mises
- wrapped normal
- wrapped Cauchy
- wrapped exponential
- wrapped asymmetric Laplace
- wrapped Lévy
- Bivariate (spherical)
- Kent
- Bivariate (toroidal)
- bivariate von Mises
- Multivariate
- von Mises–Fisher
- Bingham
and singular
- Degenerate
- Dirac delta function
- Singular
- Cantor
- Category
- Commons