Matrix-exponential distribution

Absolutely continuous distribution with rational Laplace–Stieltjes transform From Wikipedia, the free encyclopedia

In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace–Stieltjes transform.[1] They were first introduced by David Cox in 1955 as distributions with rational Laplace–Stieltjes transforms.[2]

Quick Facts Parameters, Support ...
Matrix-exponential
Parameters α, T, s
Support x ∈ [0, ∞)
PDF α ex Ts
CDF 1 + αexTT−1s
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The probability density function is (and 0 when x < 0), and the cumulative distribution function is [3] where 1 is a vector of 1s and

There are no restrictions on the parameters α, T, s other than that they correspond to a probability distribution.[4] There is no straightforward way to ascertain if a particular set of parameters form such a distribution.[2] The dimension of the matrix T is the order of the matrix-exponential representation.[1]

The distribution is a generalisation of the phase-type distribution.

Moments

If X has a matrix-exponential distribution then the kth moment is given by[2]

Fitting

Matrix exponential distributions can be fitted using maximum likelihood estimation.[5]

Software

See also

References

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