Multivariate matrix-exponential distributions

Bladt, Mogens; Nielsen, Bo Friis

doi:10.4230/DagSemProc.07461.10

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Multivariate matrix-exponential distributions

Authors Mogens Bladt, Bo Friis Nielsen

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 7461
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2008-04-07

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Document Identifiers

DOI: 10.4230/DagSemProc.07461.10
URN: urn:nbn:de:0030-drops-13975

Subject Classification

Keywords

Multivariate matrix-exponential distributions
multivariate phase-type distributions
rational Laplace transform

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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.

Cite As Get BibTex

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

Author Details

Mogens Bladt

Bo Friis Nielsen

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