Erlang Distribution

Given a Poisson distribution with a rate of change lambda, the distribution function D(x) giving the waiting times until the hth Poisson event is


for x in [0,infty), where Gamma(x) is a complete gamma function, and Gamma(a,x) an incomplete gamma function. With h explicitly an integer, this distribution is known as the Erlang distribution, and has probability function


It is closely related to the gamma distribution, which is obtained by letting alpha=h (not necessarily an integer) and defining theta=1/lambda. When h=1, it simplifies to the exponential distribution.

Evans et al. (2000, p. 71) write the distribution using the variables b=1/lambda and c=h.

See also

Exponential Distribution, Gamma Distribution, Poisson Distribution

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Evans, M.; Hastings, N.; and Peacock, B. "Erlang Distribution." Ch. 12 in Statistical Distributions, 3rd ed. New York: Wiley, pp. 71-73, 2000.

Referenced on Wolfram|Alpha

Erlang Distribution

Cite this as:

Weisstein, Eric W. "Erlang Distribution." From MathWorld--A Wolfram Web Resource.

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