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Modelling heterogeneity in survival analysis by the compound Poisson distribution. (English) Zbl 0762.62031
The common multiplicative model for heterogeneity in a population considers the time to occurrence of a particular event, modelling the individual intensity by $Z\lambda \left(t\right)$ where $Z$ is an individual quantity and $\lambda \left(t\right)$ 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.
##### MSC:
 62P10 Applications of statistics to biology and medical sciences 62M05 Markov processes: estimation 60E05 General theory of probability distributions
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