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Biometrika 1986 73(2):387-396; doi:10.1093/biomet/73.2.387
© 1986 by Biometrika Trust
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Survival models for heterogeneous populations derived from stable distributions

PHILIP HOUGAARD

Biostatistical Department, Novo Research Institute Novo Allé, DK-2880 Bagsvoerd, Denmark

A new three-parameter family of distributions on the positive numbers is proposed. It includes the stable distributions on the positive numbers, the gamma, the degenerate and the inverse Gaussian distributions. The family is characterized by the Laplace transform, from which moments, convolutions, infinite divisibility, unimodality and other properties are derived. The density is complicated, but a simple saddlepoint approximation is provided. Weibull and Gompertz distributions are naturally mixed over some of the distributions. The family is natural exponential in one of the parameters. The distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations. Desirable properties of such distributions are discussed. As an example survival after myocardial infarction is considered.

Key Words: Frailty • Gamma distribution • Heterogeneity • Inverse Gaussian distribution • Life table • Mixture • Power variance function • Saddlepoint approximation


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