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.
Publié le : 1982-02-14
Classification:
Phase type distributions,
Markov process,
closure theorems in reliability theory,
coherent systems,
60K10,
60J25
@article{1176993932,
author = {Assaf, David and Levikson, Benny},
title = {Closure of Phase Type Distributions Under Operations Arising in Reliability Theory},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 265-269},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993932}
}
Assaf, David; Levikson, Benny. Closure of Phase Type Distributions Under Operations Arising in Reliability Theory. Ann. Probab., Tome 10 (1982) no. 4, pp. 265-269. http://gdmltest.u-ga.fr/item/1176993932/