Matrix-exponential distributions: Calculus and interpretations via flows

Matrix-exponential distributions: Calculus and interpretations via flows

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Article ID: iaor2004864
Country: United States
Volume: 19
Issue: 1
Start Page Number: 113
End Page Number: 124
Publication Date: Jan 2003
Journal: Communications in Statistics - Stochastic Models
Authors: ,
Keywords: stochastic processes
Abstract:

By considering randomly stopped deterministic flow models, we develop an intuitively appealing way to generate probability distributions with rational Laplace–Stieltjes transforms on [0, ∞). That approach includes and generalizes and formalism of PH-distributions. That generalization results in the class of matrix-exponential probability distributions. To illustrate the novel way of thinking that is required to use these in stochastic models, we retrace the derivations of some results from matrix-exponential renewal theory and prove a new extension of a result from risk theory. Essentially the flow models allows for keeping track of the dynamics of a mechanism that generates matrix-exponential distributions in a similar way to the probabilistic arguments used for phase-type distributions involving transition rates. We also sketch a generalization of the Markovian arrival process (MAP) to the setting of matrix-exponential distribution. That process is known as the Rational arrival process.

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