David Assaf, Naftali A. Langberg, Thomas H. Savits, Moshe Shaked

Research output: Contribution to journalArticlepeer-review


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 study introduces and discusses several extensions to the multivariable 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.

Original languageEnglish
Pages (from-to)688-702
Number of pages15
JournalOperations Research
Issue number3
StatePublished - 1984

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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