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A bivariate Gompertz–Makeham life distribution

Author

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  • Marshall, Albert W.
  • Olkin, Ingram

Abstract

In the context of actuarial science, Gompertz (1825) utilized a differential equation to derive the life distribution that carries his name. Subsequently, De Morgan (1860), Woolhouse (1863), and Kaminsky (1983) derived the Gompertz distribution from functional equations. This paper focuses on bivariate versions of Kaminsky’s functional equation. A limiting version yields the bivariate exponential distribution of Marshall and Olkin (1967).

Suggested Citation

  • Marshall, Albert W. & Olkin, Ingram, 2015. "A bivariate Gompertz–Makeham life distribution," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 219-226.
    • Handle: RePEc:eee:jmvana:v:139:y:2015:i:c:p:219-226
    DOI: 10.1016/j.jmva.2015.02.011
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    References listed on IDEAS

    as
    1. Marshall, Albert W., 1975. "Some comments on the hazard gradient," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 293-300, July.
    2. Kundu, Debasis & Franco, Manuel & Vivo, Juana-Maria, 2014. "Multivariate distributions with proportional reversed hazard marginals," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 98-112.
    3. Samia Adham & Stephen Walker, 2001. "A multivariate Gompertz-type distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(8), pages 1051-1065.
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    Cited by:

    1. Kolev, Nikolai, 2016. "Characterizations of the class of bivariate Gompertz distributions," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 173-179.
    2. 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.

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