TOPICS
Erlang Distribution
Given a Poisson distribution with a rate of change 
,
the distribution function 
giving the waiting times until the 
th Poisson event is
 |  |  |
(1)
|
 |  |  |
(2)
|
for 
,
where 
is a complete gamma function, and 
an incomplete
gamma function. With 
explicitly an integer, this distribution is known as the Erlang
distribution, and has probability function
 |
(3)
|
It is closely related to the gamma distribution, which is obtained by letting 
(not necessarily an integer) and defining 
. When 
, it simplifies to the exponential
distribution.
Evans et al. (2000, p. 71) write the distribution using the variables 
and 
.
See also
Exponential Distribution, Gamma Distribution, Poisson DistributionExplore with Wolfram|Alpha
References
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 DistributionCite this as:
Weisstein, Eric W. "Erlang Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ErlangDistribution.html