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Characterizations of classes of lifetime distributions generalizing the NBUE class

Part of: Survival analysis and censored data Distribution theory Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Bernhard Klar  and
Alfred Müller
Bernhard Klar*
Affiliation:
Universität Karlsruhe
Alfred Müller*
Affiliation:
Universität Karlsruhe
*
∗ Postal address: Institut für Mathematische Stochastik, Universität Karlsruhe, Kaiserstr. 12, D-76128 Karlsruhe, Germany. Email address: [email protected]
∗∗ Postal address: Institut für Wirtschaftstheorie und Operations Research, Universität Karlsruhe, Kaiserstr. 12, D-76128 Karlsruhe, Germany.
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Abstract

We introduce a new class of lifetime distributions exhibiting a notion of positive ageing, called the ℳ-class, which is strongly related to the well-known ℒ-class. It is shown that distributions in the ℳ-class cannot have an undesirable property recently observed in an example of an ℒ-class distribution by Klar (2002). Moreover, it is shown how these and related classes of life distributions can be characterized by expected remaining lifetimes after a family of random times, thus extending the notion of NBUE. We give examples of ℳ-class distributions by using simple sufficient conditions, and we derive reliability bounds for distributions in this class.

Keywords

Ageingℒ-classℳ-classNBUEreliability boundsstochastic orderingmoment generating function

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60E15: Inequalities; stochastic orderings 62E10: Characterization and structure theory 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 20 - 32
Copyright
Copyright © Applied Probability Trust 2003 

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