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Log-concavity and other concepts of bivariate increasing failure rate distributions

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

Published online by Cambridge University Press:  08 February 2022

Ramesh C. Gupta Open the ORCID record for Ramesh C. Gupta [Opens in a new window]  and
S. N. U. A. Kirmani
Ramesh C. Gupta*
Affiliation:
University of Maine
S. N. U. A. Kirmani*
Affiliation:
University of Northern Iowa
*
*Postal address: University of Maine, Orono, Maine, ME 04469, USA. Email address: rcgupta@maine.edu
**Postal address: University of Northern Iowa, Cedar Falls, Iowa, IA 50614, USA. Email address: kirmani@math.uni.edu
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Abstract

Log-concavity of a joint survival function is proposed as a model for bivariate increasing failure rate (BIFR) distributions. Its connections with or distinctness from other notions of BIFR are discussed. A necessary and sufficient condition for a bivariate survival function to be log-concave (BIFR-LCC) is given that elucidates the impact of dependence between lifetimes on ageing. Illustrative examples are provided to explain BIFR-LCC for both positive and negative dependence.

Keywords

Clayton’s measure of associationhazard gradientHessian matrixlocal dependence functionlog-concave densitySchur-concavity

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60G09: Exchangeability 90B25: Reliability, availability, maintenance, inspection
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 2 , June 2022 , pp. 325 - 337
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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