Abstract
The two-parameter Weibull has been the most popular distribution for modeling lifetime data. We propose a four-parameter gamma extended Weibull model, which generalizes the Weibull and extended Weibull distributions, among several other models. We obtain explicit expressions for the ordinary and incomplete moments, generating and quantile functions and mean deviations. We employ the method of maximum likelihood for estimating the model parameters. We propose a log-gamma extended Weibull regression model with censored data. The applicability of the new models is well justified by means of two real data sets.
Highlights
There are hundreds of continuous univariate distributions and recent developments focus on constructing general distributions from classic ones
We propose a further generalization by taking the extended Weibull (EW) distribution as the baseline model
The exponentiated extended Weibull (EEW) distribution is defined by raising the cdf (2) to a power a > 0 and the associated random variable is denoted by Y ∼ EEW(τ, a)
Summary
There are hundreds of continuous univariate distributions and recent developments focus on constructing general distributions from classic ones. One of the first extensions allowing for non-monotone hazard rates, including the bathtub shaped hazard rate function (hrf ), is the exponentiated Weibull (ExpW) (Mudholkar and Srivastava 1993; Mudholkar et al 1995; and Mudholkar et al 1996) distribution. It has been well established in the literature that the ExpW distribution provides significantly better fits than the well-known exponential, gamma, Weibull and log-normal distributions.
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