Advances and Applications in Statistics
Volume 6, Issue 1, Pages 41 - 52
(April 2006)
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ON THE GAMMA FRAILTY MODEL
Theodora Dimitrakopoulou (Greece), Konstantinos Adamidis (Greece) and Sotirios Loukas (Greece)
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Abstract: One of the ways of assessing the impact of heterogeneity in mortality studies is via the concept of ?frailty?, introduced by Vaupel et al. [Demography 16 (1979), 439-454]. When the multiplicative frailty model is under consideration (see, for instance, Vaupel [Kindred lifetimes: frailty models in population genetics, Convergent Issues in Genetics and Demography, J. Adams, D. A. Lam, A. I. Herman and P. E. Smouse, eds., pp. 156-170, Oxford University Press, London, 1990]), the assumption of a gamma distributed frailty leads to the so-called gamma frailty model. This paper is devoted to exploiting some aspects of its relevant distribution theory; failure rate characterizations are obtained and bounds on the survival function are constructed. Moreover, it is shown that the model can serve as a method of constructing lifetime models or extending existing ones (by adding a parameter in the sense of Marshall and Olkin [Biometrika 84 (1997), 641-652]). |
Keywords and phrases: gamma distribution, gamma frailty model, frailty theory, lifetime distributions, mean residual lifetime, hazard rate, heterogeneity, survival function. |
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