A Log-Linear Regression Model for the Beta-Weibull Distribution

Abstract

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Keywords:

• Beta Weibull distribution
• Censored data
• Log-Weibull regression
• Residual analysis
• Sensitivity analysis
• Survival function

Mathematics Subject Classification:

• 62E15
• 62F10
• 62F40
• 62J05
• 62J20
• 62N01

Acknowledgment

This work was supported by CNPq and CAPES. We thank two referees, the Associate Editor, and the Editor for all their suggestions and comments to improve the manuscript.