Multivariate Phase-Type Distributions

David Assaf, Naftali A. Langberg, Thomas H. Savits and Moshe Shaked
Additional contact information
David Assaf: Hebrew University, Jerusalem, Israel
Naftali A. Langberg: Haifa University, Haifa, Israel
Thomas H. Savits: University of Pittsburgh, Pittsburgh, Pennsylvania
Moshe Shaked: University of Arizona, Tucson, Arizona

Operations Research, 1984, vol. 32, issue 3, 688-702

Abstract: A (univariate) random variable is said to be of phase type if it can be represented as the time until absorption in a finite state absorbing Markov chain. Univariate phase type random variables are useful because they arise from processes that are often encountered in applications, they have densities that can be written in a closed form, they possess some useful closure properties, and they can approximate any nonnegative random variable. This paper introduces and discusses several extensions to the multivariate case. It shows that the multivariate random variables possess many of the properties of univariate phase type distributions and derives explicit formulas for various probabilistic quantities of interest. Some examples are included.

Keywords: 723 absorption/failure times in Markov processes; 725 joint distribution of failure times of dependent components (search for similar items in EconPapers)
Date: 1984
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Citations: View citations in EconPapers (19)

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