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Survival models for heterogeneous populations derived from stable distributions. (English) Zbl 0603.62015

Ordinary life table methods assume that the population under study is homogeneous, but it is often more realistic to consider the population as a mixture of individuals with different hazards, the heterogeneity being described by a quantity known as the frailty. A new three-parameter family of distributions on the positive numbers is proposed as a natural model for the frailty. It includes the stable distributions, the gamma, the degenerate and the inverse Gaussian distributions. A number of properties and characterizations are given. Finally, as an example, survival after myocardial infarction is considered.
Reviewer: G.Broström

MSC:

62E10 Characterization and structure theory of statistical distributions
60E99 Distribution theory
60E07 Infinitely divisible distributions; stable distributions
62P05 Applications of statistics to actuarial sciences and financial mathematics
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