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- W1967297415 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 the 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 (RAP)." @default.
- W1967297415 created "2016-06-24" @default.
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- W1967297415 date "2003-01-04" @default.
- W1967297415 modified "2023-10-12" @default.
- W1967297415 title "Matrix‐Exponential Distributions: Calculus and Interpretations via Flows" @default.
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- W1967297415 doi "https://doi.org/10.1081/stm-120018141" @default.
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