probability theory Probability theory or probability calculus 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 expre ...

, a hyper-Erlang distribution is a

continuous probability distribution In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...

which takes a particular

Erlang distribution The Erlang distribution is a two-parameter family of continuous probability distributions with Support (mathematics), support x \in [0, \infty). The two parameters are: * a positive integer k, the "shape", and * a positive real number \lambda, ...

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