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Generalized Measures of Divergence in Survival Analysis and Reliability

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

Published online by Cambridge University Press:  14 July 2016

Filia Vonta  and
Alex Karagrigoriou
Filia Vonta*
Affiliation:
National Technical University of Athens
Alex Karagrigoriou*
Affiliation:
University of Cyprus
*
∗Postal address: Department of Mathematics, National Technical University of Athens, 9 Iroon Polytechneiou, Zografou Campus, 15780 Athens, Greece. Email address: [email protected]
∗∗Postal address: Department of Mathematics and Statistics, University of Cyprus, University Campus, CY-1678 Nicosia, Cyprus.
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Abstract

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Measures of divergence or discrepancy are used either to measure mutual information concerning two variables or to construct model selection criteria. In this paper we focus on divergence measures that are based on a class of measures known as Csiszár's divergence measures. In particular, we propose a measure of divergence between residual lives of two items that have both survived up to some time t as well as a measure of divergence between past lives, both based on Csiszár's class of measures. Furthermore, we derive properties of these measures and provide examples based on the Cox model and frailty or transformation model.

Keywords

Divergence measureCsiszár's family of measuresCox modelproportional reverse hazards modelfrailty model

MSC classification

Secondary: 62N05: Reliability and life testing 60E15: Inequalities; stochastic orderings 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 216 - 234
Copyright
Copyright © Applied Probability Trust 2010 

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