Modifications of the Weibull distribution: A review

It is well known that the Weibull distribution is the most popular and the most widely used distribution in reliability and in analysis of lifetime data. Unfortunately, its hazard function cannot exhibit non-monotonic shapes like the bathtub shape or the unimodal shape. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. This paper gives an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution.