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Zbl 0762.62031
Aalen, Odd O.
Modelling heterogeneity in survival analysis by the compound Poisson distribution. (English)
[J] Ann. Appl. Probab. 2, No.4, 951-972 (1992). ISSN 1050-5164

The common multiplicative model for heterogeneity in a population considers the time to occurrence of a particular event, modelling the individual intensity by $Z\lambda(t)$ where $Z$ is an individual quantity and $\lambda(t)$ a basic intensity. $Z$ is considered as a random variable over the population of individuals and in this paper $Z$ is assumed to be compound Poisson with subordinated gamma distribution. The atom in 0 incorporates a nonsusceptible group into the model. The population survival function and the corresponding population intensity are derived. Moreover, two examples are given where the model is fitted to data concerning marriage rates and fertility.
[C.Klüppelberg (Mannheim)]

MSC 2000:: *62P10 Appl. of statistics to biology
62M05 Markov processes: estimation
60E05 General theory of probability distributions

Keywords: hazard rates; random proportionality factor; compound Poisson distribution; subgroup of zero susceptibility; medicine; demography; forever survival; frailty; survival analysis; common multiplicative model for heterogeneity; subordinated gamma distribution; population survival function; population intensity; marriage rates; fertility

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Zentralblatt MATH Berlin [Germany]