DagSemProc.07461.10.pdf
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Multivariate matrix-exponential distributions
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Dagstuhl Seminar Proceedings, Volume 7461
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2008-04-07
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Mogens Bladt and Bo Friis Nielsen. Multivariate matrix-exponential distributions. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/DagSemProc.07461.10
https://doi.org/10.4230/DagSemProc.07461.10
Abstract
We review what is currently known about one-dimensional distributions on
the non-negative reals with rational Laplace transform, also known as
matrix-exponential distributions. In particular we discuss a flow
interpreation which enables one to mimic certain probabilisticly
inspired arguments which are known from the theory of phase-type distributions.
We then move on to present ongoing research for higher dimensions.
We discuss a characterization result, some closure properties, and
a number of examples. Finally we present open problems and future
perspectives.
Keywords
- Multivariate matrix-exponential distributions
- multivariate phase-type distributions
- rational Laplace transform
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