Multivariate matrix-exponential distributions

Authors Mogens Bladt, Bo Friis Nielsen

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Mogens Bladt
Bo Friis Nielsen

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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)


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


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