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Generalized Marshall-Olkin distributions and related bivariate aging properties

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  • Li, Xiaohu
  • Pellerey, Franco

Abstract

A class of generalized bivariate Marshall-Olkin distributions, which includes as special cases the Marshall-Olkin bivariate exponential distribution and the Marshall-Olkin type distribution due to Muliere and Scarsini (1987) [19] are examined in this paper. Stochastic comparison results are derived, and bivariate aging properties, together with properties related to evolution of dependence along time, are investigated for this class of distributions. Extensions of results previously presented in the literature are provided as well.

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  • Li, Xiaohu & Pellerey, Franco, 2011. "Generalized Marshall-Olkin distributions and related bivariate aging properties," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1399-1409, November.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:10:p:1399-1409
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    References listed on IDEAS

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    1. Navarro, Jorge & Balakrishnan, N., 2010. "Study of some measures of dependence between order statistics and systems," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 52-67, January.
    2. Asimit, Alexandru V. & Furman, Edward & Vernic, Raluca, 2010. "On a multivariate Pareto distribution," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 308-316, April.
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    Cited by:

    1. Sabrina Mulinacci, 2022. "A Marshall-Olkin Type Multivariate Model with Underlying Dependent Shocks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2455-2484, December.
    2. Sloot Henrik, 2020. "The deFinetti representation of generalised Marshall–Olkin sequences," Dependence Modeling, De Gruyter, vol. 8(1), pages 107-118, January.
    3. Sabrina Mulinacci, 2015. "Archimedean-based Marshall-Olkin Distributions and Related Copula Functions," Papers 1502.01912, arXiv.org.
    4. Gwo Dong Lin & Xiaoling Dou & Satoshi Kuriki, 2019. "The Bivariate Lack-of-Memory Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 273-297, December.
    5. Somayeh Ashrafi & Majid Asadi & Razieh Rostami, 2024. "On preventive maintenance of k-out-of-n systems subject to fatal shocks," Journal of Risk and Reliability, , vol. 238(2), pages 291-303, April.
    6. Boyan Dimitrov & Vladimir Rykov & Tatiana Milovanova, 2020. "Renewal Redundant Systems Under the Marshall–Olkin Failure Model. A Probability Analysis," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    7. Hyunju Lee & Ji Hwan Cha, 2021. "A general multivariate new better than used (MNBU) distribution and its properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 27-46, January.
    8. Jayme Pinto & Nikolai Kolev, 2016. "A class of continuous bivariate distributions with linear sum of hazard gradient components," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-17, December.
    9. Pinto, Jayme & Kolev, Nikolai, 2015. "Sibuya-type bivariate lack of memory property," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 119-128.
    10. Pellerey, Franco & Shaked, Moshe & Yasaei Sekeh, Salimeh, 2012. "Comparisons of concordance in additive models," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2059-2067.
    11. Yinping You & Xiaohu Li & Narayanaswamy Balakrishnan, 2014. "On extremes of bivariate residual lifetimes from generalized Marshall–Olkin and time transformed exponential models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 1041-1056, November.
    12. Sabrina Mulinacci, 2017. "A systemic shock model for too big to fail financial institutions," Papers 1704.02160, arXiv.org, revised Apr 2017.
    13. Matthias Scherer & Henrik Sloot, 2019. "Exogenous shock models: analytical characterization and probabilistic construction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 931-959, November.
    14. Umberto Cherubini & Sabrina Mulinacci, 2021. "Hierarchical Archimedean Dependence in Common Shock Models," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 143-163, March.
    15. Jianhua Lin & Xiaohu Li, 2014. "Multivariate Generalized Marshall–Olkin Distributions and Copulas," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 53-78, March.
    16. Gobbi, Fabio & Kolev, Nikolai & Mulinacci, Sabrina, 2021. "Ryu-type extended Marshall-Olkin model with implicit shocks and joint life insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 342-358.
    17. Li, Yang & Sun, Jianguo & Song, Shuguang, 2012. "Statistical analysis of bivariate failure time data with Marshall–Olkin Weibull models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2041-2050.
    18. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
    19. Hugo Brango & Angie Guerrero & Humberto Llinás, 2024. "Marshall–Olkin Bivariate Weibull Model with Modified Singularity (MOBW- μ ): A Study of Its Properties and Correlation Structure," Mathematics, MDPI, vol. 12(14), pages 1-16, July.
    20. Mercier, Sophie & Pham, Hai Ha, 2017. "A bivariate failure time model with random shocks and mixed effects," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 33-51.
    21. Sloot Henrik, 2020. "The deFinetti representation of generalised Marshall–Olkin sequences," Dependence Modeling, De Gruyter, vol. 8(1), pages 107-118, January.

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