Summary 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.

Generalized Exponential Distributions

The proportional hazards model has been extensively used in the literature to model failure time data. In this paper we propose to model failure time data by F*(f) = [F(t)]θ where F(t) is the baseline distribution function and θ is a positive real number. This model gives rise to monotonic as well as non-monotonic failure rates even though the baseline failure rate is monotonic. The monotonicity of the failure rates are studied, in general, and some order relations are examined. Some examples including exponentiated Weibull, exponential, gamma and Pareto distributions are investigated in detail.

Modeling failure time data by lehman alternatives

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

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A modified Weibull distribution

On families of beta- and generalized gamma-generated distributions and associated inference

A modified Weibull extension with bathtub-shaped failure rate function

A simple generalization of the Weibull distribution is presented. The distribution is well suited for modeling bathtub failure rate lifetime data and for testing goodness-of-fit of the Weibull and negative exponential models as subhypotheses. >

D.K. Srivastava

Papers

Exponentiated Weibull family for analyzing bathtub failure-rate data