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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Félix Belzunce & Carolina Martínez-Riquelme & Magdalena Pereda, 2022. "Sufficient Conditions for Some Stochastic Orders of Discrete Random Variables with Applications in Reliability," Mathematics, MDPI, vol. 10(1), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:147-:d:717562
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    References listed on IDEAS

    as
    1. Antonio Arriaza & Félix Belzunce & Carolina Martínez-Riquelme, 2021. "Sufficient Conditions for some Transform Orders Based on the Quantile Density Ratio," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 29-52, March.
    2. Félix Belzunce & Carolina Martínez-Riquelme, 2019. "On the unimodality of the likelihood ratio with applications," Statistical Papers, Springer, vol. 60(1), pages 223-237, February.
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    Cited by:

    1. Francisco Germán Badía & María Dolores Berrade, 2022. "On the Residual Lifetime and Inactivity Time in Mixtures," Mathematics, MDPI, vol. 10(15), pages 1-20, August.

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