Statistics Analysis For Log-generalized Power Weibull Regression Models

Survival analysis is an important part of statistical analysis, which could deal with many actual data about residual life, survival time, time-related failure (such data are named lifetime data). The lifetime data are widely presented in various fields, especially in engineering and bio-medical fields. In order to analyze the lifetime data, we often use some classic life distributions such as exponential distribution, Weibull distribution, while their hazard functions have strict restrictions (such as monotonicity). But hazard function is not only monotone but also non-monotonic and bathtub-shaped. So far, many authors have studied on these data by Weibull distribution, exponentiated Weibull distribution, additive Weibull distribution and so on. Recently, the literature [1] studied the parameters estimation of generalized power Weibull distribution. As a complement, this article proposes the log-generalized-power-Weibull regression models based on the generalized power Weibull distribution.In addition, Influence diagnostics have become an important part of statistical analysis, which could ensure that statistical inference is reasonable. This paper first study the parameters estimation of the log-generalized-power-Weibull regression model and obtain the maximum likelihood estimators (MLEs). The global influence analysis is studied from the case deletion model (CDM) and mean-shift model(MSOM). At the same time, the one-step approximations of the MLEs, Generalized Cook’s distance, WK measures and Likelihood distance in the case-deletion model (CDM) are given, then outlier tests are presented based on the MSOM. Meanwhile the equivalence between the CDM and MSOM is presented. Furthermore, the normal curvatures of local influence are derived under various perturbation schemes including case-weights perturbation, response variable perturbation and explanatory variable perturbation. Finally, the assumptions in the model are checked by residual analysis, such as martingale residuals, martingale-type residuals and modified martingale-type residuals. In addition, each part of the paper has been illustrated by a real data and some simulated examples.