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Transition Times: Distributions Arising from Time Heterogeneous Poisson Processes

Author

Listed:
  • 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)

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.

Suggested Citation

  • Peter J. Lenk & Ambar G. Rao, 1995. "Transition Times: Distributions Arising from Time Heterogeneous Poisson Processes," Management Science, INFORMS, vol. 41(7), pages 1117-1129, July.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:7:p:1117-1129
    DOI: 10.1287/mnsc.41.7.1117
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    Cited by:

    1. Zhuoxin Li & Jason A. Duan & Sam Ransbotham, 2020. "Coordination and Dynamic Promotion Strategies in Crowdfunding with Network Externalities," Production and Operations Management, Production and Operations Management Society, vol. 29(4), pages 1032-1049, April.
    2. Chien-Chou Chen & Guo-Jun Lo & Ta-Chien Chan, 2022. "Spatial Analysis on Supply and Demand of Adult Surgical Masks in Taipei Metropolitan Areas in the Early Phase of the COVID-19 Pandemic," IJERPH, MDPI, vol. 19(11), pages 1-12, May.
    3. Zhuoxin Li & Jason A. Duan, 2014. "Dynamic Strategies for Successful Online Crowdfunding," Working Papers 14-09, NET Institute.

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