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

10.6339/JDS.2013.11(4).1131

Marcelino A. R. Pascoa；Claudia M. M. de Paiva；Gauss M. Cordeiro；Edwin M. M. Ortega

Censored data ； generating function ； Kumaraswamy generalized gamma distribution ； log-gamma generalized regression ； moment ； survival function

Journal of Data Science

11卷4期（2013 / 10 / 01）

781 - 818

英文

The five parameter Kumaraswamy generalized gamma model (Pascoa 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, bathtub and unimodal shaped hazard functions. A second advantage is that it also includes as special models reciprocal distributions such as the reciprocal gamma and reciprocal Weibull distributions. A third advantage is that it can represent the error distribution for the log-Kumaraswamy generalized 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 effectively in the analysis of survival data since it includes as submodels several widely-known regression models. The method of maximum likelihood and a Bayesian procedure are used for estimating the model parameters for censored data. Overall, the new regression model is very useful to the analysis of real data.