A unified view on lifetime distributions arising from selection mechanisms

For the first time, we formulate a flexible density function from the selection mechanism viewpoint (see, for example, Bayarri & DeGroot (1992) and ArellanoValle et al. (2006)) which possesses nice biological and physical interpretations. The new density function contains as special cases many models that have been proposed recently in the literature. In our model, we assume that the number of competing causes of the event of interest has a general discrete distribution characterized by its probability generating function. This function has an important role in the selection procedure as well as in computing the conditional personal cure rate. We illustrate how various models can be deduced as special cases of the proposed model.