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Entropy-based measure of uncertainty in past lifetime distributions

Part of: Survival analysis and censored data Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Antonio Di Crescenzo  and
Maria Longobardi
Antonio Di Crescenzo*
Affiliation:
Università della Basilicata
Maria Longobardi*
Affiliation:
Università di Napoli Federico II
*
∗ Current address: Dipartimento di Matematica e Informatica, Università di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy. Email address: adicrescenzo@unisa.it
∗∗ Postal address: Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy.
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Abstract

As proposed by Ebrahimi, uncertainty in the residual lifetime distribution can be measured by means of the Shannon entropy. In this paper, we analyse a dual characterization of life distributions that is based on entropy applied to the past lifetime. Various aspects of this measure of uncertainty are considered, including its connection with the residual entropy, the relation between its increasing nature and the DRFR property, and the effect of monotonic transformations on it.

Keywords

Residual lifetimereversed hazard functionDRFR propertymonotonic transformation

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 434 - 440
Copyright
Copyright © Applied Probability Trust 2002 

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