A family of cumulative hazard functions and their frailty connections

Karim Anaya-Izquierdo, Alice Davis, Michael Christopher Jones

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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 bivariate case. We also suggest how best to incorporate a second, complementary, shape parameter in order to obtain especially useful parametric models for survival and reliability analysis.

Original languageEnglish
Article number109059
JournalStatistics and Probability Letters
Early online date18 Feb 2021
Publication statusPublished - 31 May 2021

Bibliographical note

Funding Information:
Alice Davis was supported by a UK EPSRC DTA doctoral studentship at the University of Bath.

Publisher Copyright:
© 2021 Elsevier B.V.


  • Archimedean survival copula
  • Parametric survival analysis
  • Proportionality parameter
  • Reliability analysis
  • Shared frailty

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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