License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07461.10
URN: urn:nbn:de:0030-drops-13975
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1397/
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Bladt, Mogens ; Nielsen, Bo Friis

Multivariate matrix-exponential distributions

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07461.NielsenBoFriis.Paper.1397.pdf (0.1 MB)

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.


BibTeX - Entry

@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/opus/volltexte/2008/1397},
  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}
}

Keywords: Multivariate matrix-exponential distributions, multivariate phase-type distributions, rational Laplace transform
Collection: 07461 - Numerical Methods for Structured Markov Chains
Issue Date: 2008
Date of publication: 07.04.2008

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