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A note on the ℒ-class of life distributions

Part of: Distribution theory - Probability Operations research and management science Integral transforms, operational calculus

Published online by Cambridge University Press:  14 July 2016

B. Klar
B. Klar*
Affiliation:
Universität Karlsruhe
*
∗ Postal address: Institut für Mathematische Stochastik, Universität Karlsruhe, Englerstr. 2, 76128 Karlsruhe, Germany. Email address: bernhard.klar@math.uni-karlsruhe.de
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Abstract

This paper first recalls some stochastic orderings useful for studying the ℒ-class and the Laplace order in general. We use these orders to show that the higher moments of an ℒ-class distribution need not exist. Using simple sufficient conditions for the Laplace ordering, we give examples of distributions in the ℒ- and ℒα-classes. Moreover, we present explicit sharp bounds on the survival function of a distribution belonging to the ℒ-class of life distributions. The results reveal that the ℒ-class should not be seen as a more comprehensive class of ageing distributions but rather as a large class of life distributions on its own.

Keywords

Laplace orders-(increasing) convex orders-(increasing) concave orderℒα-classreliability boundslife distribution

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 44A10: Laplace transform 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 11 - 19
Copyright
Copyright © Applied Probability Trust 2002 

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