Log-Burr XII Gamma–Weibull Regression Model with Random Effects and Censored Data

Abstract

It may happen in some applications that the assumption of independence of survival times does not hold. Thus, we propose a new log-Burr XII regression model with log-gamma–Weibull distributions for the random effects. The maximum likelihood method is used to estimate the model parameters based on the Gauss–Hermite numerical integration technique. For different parameter settings, sample sizes, censoring percentages and correlated data, various simulations are performed. Some global-influence measurements are also investigated. In order to assess the robustness of the maximum likelihood estimators, we evaluate local influence on the estimates of the parameters under different perturbation schemes. We illustrate the importance of the new model by means of a real data set in analysis of experiments.