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Stochastic orders based on ratios of Laplace transforms

Part of: Special processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Moshe Shaked  and
Tityik Wong
Moshe Shaked*
Affiliation:
University of Arizona
Tityik Wong*
Affiliation:
Community College of Southern Nevada
*
∗Postal address: Department of Mathematics, Building #89, University of Arizona, Tucson, Arizona 85721, USA.
∗∗Postal address: Department of Mathematics, Community College of Southern Nevada, 3200 E. Cheyenne Ave-SIA, North Las Vegas, Nevada 89030, USA.
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Abstract

The purpose of this paper is to study two notions of stochastic comparisons of non-negative random variables via ratios that are determined by their Laplace transforms. Some interpretations of the new orders are given, and various properties of them are derived. The relationships to other stochastic orders are also studied. Finally, some applications in reliability theory are described.

Keywords

PRESERVATION PROPERTIESINCREASING CONVEX ORDERINCREASING CONCAVE ORDERHAZARD RATE ORDERREVERSE HAZARD RATE ORDERLIKELIHOOD RATIO ORDERUSUAL STOCHASTIC ORDERLAPLACE TRANSFORMLAPLACE TRANSFORM ORDERRANDOM MINIMA AND MAXIMARELIABILITY THEORY

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 404 - 419
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Supported by NSF Grant DMS 9303891.

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