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Multivariate matrix-exponential distributions

Authors: Mogens Bladt and Bo Friis Nielsen

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

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.

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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)

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@InProceedings{bladt_et_al:DagSemProc.07461.10,
  author =	{Bladt, Mogens and Nielsen, Bo Friis},
  title =	{{Multivariate matrix-exponential distributions}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.10},
  URN =		{urn:nbn:de:0030-drops-13975},
  doi =		{10.4230/DagSemProc.07461.10},
  annote =	{Keywords: Multivariate matrix-exponential distributions, multivariate phase-type distributions, rational Laplace transform}
}

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Multivariate matrix-exponential distributions

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