Sufficient Conditions for Some Stochastic Orders of Discrete Random Variables with Applications in Reliability

Félix Belzunce, Carolina Martínez-Riquelme and Magdalena Pereda
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Félix Belzunce: Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
Carolina Martínez-Riquelme: Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
Magdalena Pereda: Collège Sciences et Technologies pour l’Energie et l’Environnement (STEE), Université de Pau et des Pays de L’Adour, Avenue de l’Université, CEDEX, BP576-64012 Pau, France

Mathematics, 2022, vol. 10, issue 1, 1-15

Abstract: In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the unimodality of the likelihood ratio for the comparison in some stochastic orders of two discrete random variables. These results have interest in comparing discrete random variables because the sufficient conditions are easy to check when there are no closed expressions for the survival functions, which occurs in many cases. In addition, the results are applied to compare several parametric families of discrete distributions.

Keywords: stochastic orders; discrete distributions; unimodality; panjer; generalized Poisson; discrete Weibull; Hurwitz-Lerch family (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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