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February, 1982 Closure of Phase Type Distributions Under Operations Arising in Reliability Theory
David Assaf, Benny Levikson
Ann. Probab. 10(1): 265-269 (February, 1982). DOI: 10.1214/aop/1176993932

Abstract

Consider three basic operations arising in reliability theory: finite mixtures, finite convolutions, formation of coherent systems of independent components. In this paper it is shown that: (i) The class of all phase type distributions is closed under all three operations; (ii) the class of all phase type distributions having a representation in which the matrix is upper triangular is the smallest class which is closed under all three operations and contains all exponential distributions. The paper includes a section of preliminaries in which the relevant material regarding phase type distributions and reliability theory is summarized.

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David Assaf. Benny Levikson. "Closure of Phase Type Distributions Under Operations Arising in Reliability Theory." Ann. Probab. 10 (1) 265 - 269, February, 1982. https://doi.org/10.1214/aop/1176993932

Information

Published: February, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0479.60085
MathSciNet: MR637395
Digital Object Identifier: 10.1214/aop/1176993932

Subjects:
Primary: 60K10
Secondary: 60J25

Keywords: closure theorems in reliability theory , coherent systems , Markov process , Phase type distributions

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 1 • February, 1982
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