Hougaard, Philip Survival models for heterogeneous populations derived from stable distributions. (English) Zbl 0603.62015 Biometrika 73, 387-396 (1986). 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 Cited in 4 ReviewsCited in 190 Documents 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 Keywords:Laplace transform; saddlepoint approximation; degenerate distributions; life table methods; heterogeneity; frailty; new three-parameter family of distributions; stable distributions; gamma; inverse Gaussian distributions; characterizations; myocardial infarction PDFBibTeX XMLCite \textit{P. Hougaard}, Biometrika 73, 387--396 (1986; Zbl 0603.62015) Full Text: DOI