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On some stochastic comparisons of arithmetic and geometric mixture models

Author

Listed:
  • Omid Shojaee

    (University of Zabol)

  • Manoochehr Babanezhad

    (Golestan University)

Abstract

Most studies on reliability analysis have been conducted in homogeneous populations. However, homogeneous populations can rarely be found in the real world. Populations with specific components, such as lifetime, are usually heterogeneous. When populations are heterogeneous, it raises the question of whether these different modeling analysis strategies might be appropriate and which one of them should be preferred. In this paper, we provide mixture models, which have usually been effective tools for modeling heterogeneity in populations. Specifically, we carry out a stochastic comparison of two arithmetic (finite) mixture models using the majorization concept in the sense of the usual stochastic order, the hazard rate order, the reversed hazard rate order and the dispersive order both for a general case and for some semiparametric families of distributions. Moreover, we obtain sufficient conditions to compare two geometric mixture models. To illustrate the theoretical findings, some relevant examples and counterexamples are presented.

Suggested Citation

  • Omid Shojaee & Manoochehr Babanezhad, 2023. "On some stochastic comparisons of arithmetic and geometric mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 499-515, July.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:5:d:10.1007_s00184-022-00880-3
    DOI: 10.1007/s00184-022-00880-3
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    References listed on IDEAS

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    1. Francisco Germán Badía & Hyunju Lee, 2020. "On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 355-375, April.
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    3. Cha, Ji Hwan & Finkelstein, Maxim, 2013. "The failure rate dynamics in heterogeneous populations," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 120-128.
    4. Nil Kamal Hazra & Maxim Finkelstein, 2018. "On stochastic comparisons of finite mixtures for some semiparametric families of distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 988-1006, December.
    5. Bartoszewicz, J., 1987. "A note on dispersive ordering defined by hazard functions," Statistics & Probability Letters, Elsevier, vol. 6(1), pages 13-16, September.
    6. Omid Shojaee & Majid Asadi & Maxim Finkelstein, 2021. "On Some Properties of $$\alpha $$ α -Mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1213-1240, November.
    7. Jorge Navarro, 2016. "Stochastic comparisons of generalized mixtures and coherent systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 150-169, March.
    8. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, February.
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