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Erschienen in:
2013 | OriginalPaper | Buchkapitel
3. Bilateral Matrix-Exponential Distributions
verfasst von : Mogens Bladt, Luz Judith R. Esparza, Bo Friis Nielsen
Erschienen in: Matrix-Analytic Methods in Stochastic Models
Verlag: Springer New York
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Abstract
In this article we define the classes of bilateral and multivariate bilateral matrix-exponential distributions. These distributions have support on the entire real space and have rational moment-generating functions. The distributions extend the class of bilateral phase-type distributions of Ahn and Ramaswami [Stoch. Models 21, 239–259 (2005)] and the class of multivariate matrix-exponential distributions of Bladt and Nielsen [Stoch. Models 26, 1–26 (2010)]. We prove a characterization theorem stating that a random variable has a bilateral multivariate distribution if and only if all linear combinations of the coordinates have a univariate bilateral matrix-exponential distribution. As an application we demonstrate that certain multivariate diffusions, which are governed by the underlying Markov jump process generating a phase-type distribution, have a bilateral matrix-exponential distribution at the time of absorption.