The Log-Kumaraswamy Generalized Gamma Regression Model with Application to Chemical Dependency Data

Abstract

The ve parameter Kumaraswamy generalized gamma model (Pas- coa et al., 2011) includes some important distributions as special cases and it is very useful for modeling lifetime data. We propose an extended version of this distribution by assuming that a shape parameter can take negative values. The new distribution can accommodate increasing, decreasing, bath- tub and unimodal shaped hazard functions. A second advantage is that it also includes as special models reciprocal distributions such as the recipro- cal gamma and reciprocal Weibull distributions. A third advantage is that it can represent the error distribution for the log-Kumaraswamy general- ized gamma regression model. We provide a mathematical treatment of the new distribution including explicit expressions for moments, generating function, mean deviations and order statistics. We obtain the moments of the log-transformed distribution. The new regression model can be used more eectively in the analysis of survival data since it includes as sub- models several widely-known regression models. The method of maximum likelihood and a Bayesian procedure are used for estimating the model pa- rameters for censored data. Overall, the new regression model is very useful to the analysis of real data.