Statistical inference methods for recurrent event processes with shape and size parameters

Mei Cheng Wang, Chiung Yu Huang

Research output: Contribution to journalArticlepeer-review


This paper proposes a unified framework to characterize the rate function of a recurrent event process through shape and size parameters. In contrast to the intensity function, which is the event occurrence rate conditional on the event history, the rate function is the occurrence rate unconditional on the event history, and thus it can be interpreted as a population-averaged count of events in unit time. In this paper, shape and size parameters are introduced and used to characterize the association between the rate function λ(·) and a random variable X. Measures of association between X and λ(·) are defined via shape- and size-based coefficients. Rate-independence of X and λ(·) is studied through tests of shape-independence and size-independence, where the shapeand size-based test statistics can be used separately or in combination. These tests can be applied when X is a covariable possibly correlated with the recurrent event process through λ(·) or, in the one-sample setting, when X is the censoring time at which the observation of N(·) is terminated. The proposed tests are shape- and size-based so when a null hypothesis is rejected the test results can serve to distinguish the source of violation.

Original languageEnglish (US)
Pages (from-to)553-566
Number of pages14
Issue number3
StatePublished - Sep 2014


  • Intensity function
  • Point process
  • Poisson process
  • Rate function
  • Rate-independence
  • Shapeindependence
  • Size-independence

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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