Transition Times: Distributions Arising from Time Heterogeneous Poisson Processes

Peter J. Lenk and Ambar G. Rao
Additional contact information
Peter J. Lenk: School of Business Administration, University of Michigan, Ann Arbor, Michigan 48109-1234
Ambar G. Rao: Faculty of Management, University of Toronto, Toronto, Ontario, Canada M5S 1V4

Management Science, 1995, vol. 41, issue 7, 1117-1129

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 (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 \Gamma 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.

Keywords: gamma distribution; F distribution; mixture distributions; Poisson distribution; reliability (search for similar items in EconPapers)
Date: 1995
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.41.7.1117 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:41:y:1995:i:7:p:1117-1129

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().