Continuous distributions

Matrix-exponential distribution

In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace–Stieltjes transform. They were first introduced by David Cox in 1955 as distributions with rational Laplace–Stieltjes transforms. The probability density function is (and 0 when x < 0), and the cumulative distribution function is 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. There is no straightforward way to ascertain if a particular set of parameters form such a distribution. The dimension of the matrix T is the order of the matrix-exponential representation. The distribution is a generalisation of the phase-type distribution. (Wikipedia).

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From playlist Continuous Random Variables

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From playlist Systems of Differential Equations

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From playlist Ordinary Differential Equations

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From playlist Differential Equations: Complete Set of Course Videos

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From playlist Linear Algebra

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Moment (mathematics) | Maximum likelihood estimation | Laplace–Stieltjes transform | MATLAB | Rational arrival process | Probability theory | David Cox (statistician) | Probability density function | Cumulative distribution function | Phase-type distribution