Erlang Distribution

The Erlang distribution is a special case of the gamma distribution where the shape parameter is an integer.  It represents the sum of a series of exponential distributions.  To be consistent with the documentation, the terms scale and shape have been used, however, the scale is the equivalent of the mean of an exponential distribution and the scale is the number of exponentially distributed events.

The distribution resulted from work done by the Danish mathematician Agner Krarup Erlang (1878 - 1929) who was a pioneer in the application of statistical methods to the analysis of telephone networks.  The distribution was derived to model the total waiting time associated with a queue of requests on a telephone exchange.

Profile

Parameters

Parameter	Description	Characteristics
Scale	Equivalent to the mean of an exponential distribution	A float > 0
Shape	The number of exponentially distributed events.	A integer > 0

Range

From zero to positive infinity

Functions

The formula for P(x) shown below is the probability density function for the Gamma distribution with an integer shape parameter.

Where  is the incomplete gamma function.

Properties