Theory & Methods: Generalized exponential distributions

TLDR

The three‑parameter gamma and Weibull distributions are widely used for lifetime data, offering flexible hazard shapes but also possessing notable drawbacks. This paper introduces a three‑parameter distribution, a special case of the exponentiated Weibull without a location parameter, to address these limitations. The authors analyze its properties, noting similarities to the gamma and Weibull families while highlighting distinct characteristics. The model serves as a viable alternative to gamma or Weibull, fitting a sample dataset more accurately than either.

Abstract

The three‐parameter gamma and three‐parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three‐parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three‐parameter generalized exponential distribution fits better than the three‐parameter Weibull distribution or the three‐parameter gamma distribution.