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Preservation of Stochastic Orders under the Formation of Generalized Distorted Distributions. Applications to Coherent Systems

Author

Listed:
  • Jorge Navarro

    (Universidad de Murcia)

  • Yolanda Águila

    (Universidad de Almería)

  • Miguel A. Sordo

    (Universidad de Cádiz)

  • Alfonso Suárez-Llorens

    (Universidad de Cádiz)

Abstract

The preservation of stochastic orders under the formation of coherent systems is a relevant topic in the reliability theory. Several properties have been obtained under the assumption of identically distributed components. In this paper we obtain ordering preservation results for generalized distorted distributions (GDD) which, in particular, can be used to obtain preservation results for coherent systems with non-identically distributed components. We consider both the cases of independent and dependent components. The preservation results obtained here for GDD can also be applied to other statistical concepts.

Suggested Citation

  • Jorge Navarro & Yolanda Águila & Miguel A. Sordo & Alfonso Suárez-Llorens, 2016. "Preservation of Stochastic Orders under the Formation of Generalized Distorted Distributions. Applications to Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 529-545, June.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:2:d:10.1007_s11009-015-9441-z
    DOI: 10.1007/s11009-015-9441-z
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    References listed on IDEAS

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    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
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    6. Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2011. "Stochastic comparisons of distorted variability measures," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 11-17, July.
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    Citations

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    Cited by:

    1. Antonio Arriaza & Jorge Navarro & Alfonso Suárez‐Llorens, 2018. "Stochastic comparisons of replacement policies in coherent systems under minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 550-565, September.
    2. Jorge Navarro, 2018. "Distribution-free comparisons of residual lifetimes of coherent systems based on copula properties," Statistical Papers, Springer, vol. 59(2), pages 781-800, June.
    3. M. Kelkinnama & M. Asadi, 2019. "Stochastic and ageing properties of coherent systems with dependent identically distributed components," Statistical Papers, Springer, vol. 60(3), pages 805-821, June.
    4. Mansour Shrahili & Mohamed Kayid & Mhamed Mesfioui, 2023. "Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models," Mathematics, MDPI, vol. 11(22), pages 1-28, November.
    5. Siddhartha Chakraborty & Biswabrata Pradhan, 2024. "On cumulative residual extropy of coherent and mixed systems," Annals of Operations Research, Springer, vol. 340(1), pages 59-81, September.
    6. Patryk Miziuła & Jorge Navarro, 2017. "Sharp bounds for the reliability of systems and mixtures with ordered components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(2), pages 108-116, March.
    7. Jorge Navarro & Maria Longobardi & Franco Pellerey, 2017. "Comparison results for inactivity times of k-out-of-n and general coherent systems with dependent components," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 822-846, December.
    8. Jorge Navarro & Yolanda Águila, 2017. "Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 627-648, November.

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