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Presentation of phase-type distributions as proper mixtures

Published online by Cambridge University Press:  14 July 2016

David Assaf  and
Naftali A. Langberg
David Assaf*
Affiliation:
The Hebrew University, Jerusalem
Naftali A. Langberg*
Affiliation:
Haifa University
*
∗Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel.
∗∗Postal address: Department of Statistics, Haifa University, Mount Carmel, Haifa, Israel.
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Abstract

It is shown that any phase-type distribution can be represented as a proper mixture of two distinct phase-type distributions. Using different terms, it is shown that the class of phase-type distributions does not include any extreme ones. A similar result holds for the subclass of upper-triangular phase-type distributions.

Keywords

MIXTURES OF DISTRIBUTION FUNCTIONSEXTREME POINTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 247 - 250
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Research partly carried out while this author was visiting the University of Arizona.

References

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