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On stochastic dependence in residual lifetime and inactivity time with some applications

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  • Li, Chen
  • Li, Xiaohu

Abstract

For bivariate random lifetimes, we study the role of stochastic dependence through conducting stochastic comparison on the residual life, inactivity time and some aging behavior of one marginal conditioned by the survival or failure of the other. The main results serve as essential supplement to those related ones of Bassan and Spizzichino (1999) and Longobardi and Pellerey (2019). Applications in frailty, resilience and load-sharing models are presented as well.

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  • Li, Chen & Li, Xiaohu, 2021. "On stochastic dependence in residual lifetime and inactivity time with some applications," Statistics & Probability Letters, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:stapro:v:177:y:2021:i:c:s0167715221000821
    DOI: 10.1016/j.spl.2021.109120
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    References listed on IDEAS

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    1. Eeckhoudt, Louis & Gollier, Christian, 1995. "Demand for Risky Assets and the Monotone Probability Ratio Order," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 113-122, September.
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    3. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    4. Masaaki Kijima & Masamitsu Ohnishi, 1996. "Portfolio Selection Problems Via The Bivariate Characterization Of Stochastic Dominance Relations1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 237-277, July.
    5. Longobardi, Maria & Pellerey, Franco, 2019. "On the role of dependence in residual lifetimes," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 56-64.
    6. Li, Xiaohu & Fang, Rui, 2015. "Ordering properties of order statistics from random variables of Archimedean copulas with applications," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 304-320.
    7. Bassan, Bruno & Spizzichino, Fabio, 2005. "Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 313-339, April.
    8. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    Cited by:

    1. Zhang, Yiying, 2024. "Stochastic orders and distortion risk contribution ratio measures," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 104-122.

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