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New characterizations of the no-aging property and the ℓ1-isotropic model

Part of: Geometric probability and stochastic geometry Distribution theory

Published online by Cambridge University Press:  14 July 2016

Stephen E. Chick  and
Max B. Mendel
Stephen E. Chick*
Affiliation:
University of Michigan
Max B. Mendel*
Affiliation:
University of California
*
∗Postal address: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109–2117, USA. Email address: [email protected]
∗∗Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA
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Abstract

The no-aging property and the ℓ1-isotropic model it implies have been introduced to overcome certain shortcomings of the exponential model. However, its definition is abstract and not very useful for practitioners. This paper presents several additional characterizations of the no-aging property. Included are (1) characterizations that appropriately generalize the memoryless property and the constant-failure-rate property of the exponential, (2) behavioral characterizations based on fair bets, and (3) geometric characterizations of the survival and density function and differential-geometric characterizations based on tensor methods.

Keywords

No-agingℓ1-isotropic modelcharacterization of probability modelsexponential modelmemoryless propertyhazard gradientBayesian probabilitytensor methods in probability

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 903 - 910
Copyright
Copyright © Applied Probability Trust 1998 

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