Properties of classes of life distributions based on the conditional variance
Jordan Stoyanov and M. H. M. Al-Sadi
Source: J. Appl. Probab.
Volume 41, Number 4
(2004), 953-960.
Abstract
We consider two classes of life distribution,
VD and VI, the
members of which are defined in terms of the conditional variance
σ2(t) of the remaining lifetime of a
system: a life distribution F belongs to
VD if
σF2(t) is a decreasing
function and to VI if
σF2(t) is increasing.
We study closure properties of these classes under relevant
reliability operations such as mixing, convolution and formation
of coherent systems. We show, for example, that the class
VD is not closed under convolution or
mixing, and that the class VI is not
closed under formation of coherent systems.
Primary Subjects: 62N05, 90B25
Keywords: Conditional variance; decreasing-variance life distribution; increasing-variance life distribution; mixing; convolution; formation of coherent system
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1101840542
Digital Object Identifier: doi:10.1239/jap/1101840542
Mathematical Reviews number (MathSciNet):
MR2122471
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