# HypoexponentialDistribution

HypoexponentialDistribution[{λ1,,λm}]

represents an m-phase hypoexponential distribution with rates λ1, , λm.

# Details • HypoexponentialDistribution is also known as a sequential m-phase exponential distribution.
• An m-phase hypoexponential distribution can be interpreted as having m servers in series where the i server has service rate λi.
• The probability density for value and distinct rates is a linear combination of exponentials for and zero for .
• HypoexponentialDistribution[{λ1,,λm}] is equivalent to TransformedDistribution[x1++xm,] with each xi from .
• HypoexponentialDistribution allows λi to be any positive real numbers.
• HypoexponentialDistribution allows λi to be any quantities of the same unit dimensions. »
• HypoexponentialDistribution can be used with such functions as Mean, CDF, and RandomVariate.

# Examples

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## Basic Examples(4)

Probability density function:

 In:= Out= In:= Out= Cumulative distribution function:

 In:= Out= In:= Out= Mean and variance:

 In:= Out= In:= Out= Median can be found exactly in some cases:

 In:= Out= But the general closed form does not exist:

 In:= Out= ## Neat Examples(1)

Introduced in 2012
(9.0)
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Updated in 2016
(10.4)