A family of cumulative hazard functions and their frailty connections

Karim Anaya-Izquierdo, Alice Davis, Michael Christopher Jones

Research output: Contribution to journalArticlepeer-review


We consider a novel family of cumulative hazard functions (CHFs) controlled by a single shape parameter, which corresponds to proportionality on a certain scale, in such a way that the family is closed under inversion of the CHF and under frailty mixing using an appropriate mixing distribution. The latter leads to natural shared frailty models in the multivariate case. We also suggest how best to incorporate a sec- ond, complementary, shape parameter in order to obtain especially useful parametric models for survival and reliability analysis.
Original languageEnglish
JournalStatistics and Probability Letters
Publication statusAcceptance date - 22 Jan 2021


  • Archimedean survival copula
  • Parametric survival analysis
  • Proportional- ity parameter
  • Reliability analysis
  • Shared frailty

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