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URN: urn:nbn:de:0030-drops-13975
URL: https://drops.dagstuhl.de/opus/volltexte/2008/1397/
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Bladt, Mogens ; Nielsen, Bo Friis

Multivariate matrix-exponential distributions

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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:DSP:2008:1397,
  author =	{Mogens Bladt and Bo Friis Nielsen},
  title =	{Multivariate matrix-exponential distributions},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  year =	{2008},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  number =	{07461},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1397},
  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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