A new inverted u-shape hazard function

Tal Avinadav, Tzvi Raz

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The hazard function describes the unobserved rate at which failures occur. In this paper, we present a new inverted U-shape hazard function, developed for risk-events related to human activities. This hazard shape has received less attention in the literature relative to monotone hazard functions, likely due to the mathematical complexity of their regression models. We present a new survivor function, based on a logarithm transformation, and time displacement of Weibull's survivor function, that has an inverted U-shape hazard function similar to the log-logistic one. The advantage of this hazard function relative to the Weibull, and log-logistic hazard functions is in its unique curvature, which may fit better in some cases. We use simulation studies to present the new distribution characteristics in comparison to the Weibull, and the log-logistic distributions.

Original languageEnglish
Pages (from-to)32-40
Number of pages9
JournalIEEE Transactions on Reliability
Issue number1
StatePublished - Mar 2008


  • Exposure time transformation
  • Hazard function
  • Log-logistic distribution
  • Survivor function
  • Weibull distribution


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