Transition times: Distributions arising from time heterogeneous Poisson processes

Transition times: Distributions arising from time heterogeneous Poisson processes

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Article ID: iaor19961840
Country: United States
Volume: 41
Issue: 7
Start Page Number: 1117
End Page Number: 1129
Publication Date: Jul 1995
Journal: Management Science
Authors: ,
Keywords: quality & reliability, stochastic processes
Abstract:

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 ¦) (gamma) distribution. The authors 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 ¦) 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. The authors 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.

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