TRANSITION TIMES - DISTRIBUTIONS ARISING FROM TIME HETEROGENEOUS POISSON PROCESSES

The units of a heterogeneous population are subjected to shocks. A uni t fails, or more generally, undergoes a change of state after a suffic ient number of shocks. The shocks for a particular unit are assumed to arrive according to a time heterogeneous Poisson process. The time to a change of state, the transition time, for the unit has a generalize d Gamma (gamma) distribution. We assume that the intensity of the Pois son process and the number of shocks until the change of state vary in dependently across the units according to a Gamma and negative binomia l distribution, respectively. The distribution of the transition time is shown to be the generalized F distribution, which includes a number of standard distributions as special cases. We illustrate these resul ts with two empirical examples: modelling coupon redemptions and traff ic accidents. In the latter case, the intensity function of the Poisso n process includes time varying predictor variables.