Survival functions for the frailty models based on the discrete compound Poisson process

AbstractFrailty models are often used to model heterogeneity in survival analysis. The distribution of the frailty is generally assumed to be continuous. In some circumstances, it is appropriate to consider discrete frailty distributions. Having zero frailty can be interpreted as being immune, and population heterogeneity may be analysed using discrete frailty models. In this paper, survival functions are derived for the frailty models based on the discrete compound Poisson process. Maximum likelihood estimation procedures for the parameters are studied. We examine the fit of the models to earthquake and the traffic accidents' data sets from Turkey.Keywords: infinitely divisible distributionsstable distributionscensored data modelsestimationfrailty modelscompound Poisson distribution2000 Mathematics Subject Classification codes: 60E0762N0162N0265C5068U20 The authors thank the editor and anonymous referee for their constructive comments on an earlier version of this manuscript which resulted in this improved version.