probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

, a hyper-Erlang distribution is a

continuous probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...

which takes a particular

Erlang distribution The Erlang distribution is a two-parameter family of continuous probability distributions with support x \in independent exponential distribution">exponential variables with mean 1/\lambda each. Equivalently, it is the distribution of the tim ...

E_''i'' with probability ''p''_''i''. A hyper-Erlang distributed random variable ''X'' has a

probability density function In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) ca ...

given by :

A(x) = \sum_^n p_i E_(x)

where each ''p''_''i'' > 0 with the ''p''_''i'' summing to 1 and each of the E_{''l''_''i''} being an

with ''l''_''i'' stages each of which has parameter ''λ''_''i''.

References

{{ProbDistributions, continuous-semi-infinite Continuous distributions

See also

References