Transition Times: Distributions Arising from Time Heterogeneous Poisson Processes
研究异质总体中个体在时间异质泊松过程冲击下状态转变时间的分布，推导出广义F分布，并用优惠券赎回和交通事故两个例子验证模型。
The units of a heterogeneous population are subjected to shocks. A unit fails, or more generally, undergoes a change of state after a sufficient 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 generalized Γ (gamma) distribution. We assume that the intensity of the Poisson process and the number of shocks until the change of state vary independently across the units according to a Γ and negative binomial 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 results with two empirical examples: modelling coupon redemptions and traffic accidents. In the latter case, the intensity function of the Poisson process includes time varying predictor variables.