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Bounds for the hazard rate and the reversed hazard rate of the convolution of dependent random lifetimes

Part of: Distribution theory - Probability Applications

Published online by Cambridge University Press:  11 December 2019

Félix Belzunce  and
Carolina Martínez-Riquelme
Félix Belzunce*
Affiliation:
University of Murcia
Carolina Martínez-Riquelme*
Affiliation:
University of Murcia
*
*Postal address: Departamento Estadística e Investigación Operativa, Universidad de Murcia, Facultad de Matemáticas, Campus de Espinardo, 30100 Espinardo (Murcia), Spain.
*Postal address: Departamento Estadística e Investigación Operativa, Universidad de Murcia, Facultad de Matemáticas, Campus de Espinardo, 30100 Espinardo (Murcia), Spain.
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Abstract

An upper bound for the hazard rate function of a convolution of not necessarily independent random lifetimes is provided, which generalizes a recent result established for independent random lifetimes. Similar results are considered for the reversed hazard rate function. Applications to parametric and semiparametric models are also given.

Keywords

Reliabilityhazard rate functionreversed hazard rate functionconvolutiondependent random lifetime

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 4 , December 2019 , pp. 1033 - 1043
Copyright
© Applied Probability Trust 2019 

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