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The log-generalized modified Weibull regression model. (English) Zbl 1300.62019
Summary: For the first time, we introduce the log-generalized modified Weibull regression model based on the modified Weibull distribution [J. M. F. Carrasco et al., Comput. Stat. Data Anal. 53, No. 2, 450–462 (2008; Zbl 1231.62015)]. This distribution can accommodate increasing, decreasing, bathtub and unimodal shaped hazard functions. A second advantage is that it includes classical distributions reported in lifetime literature as special cases. We also show that the new regression model can be applied to censored data since it represents a parametric family of models that includes as submodels several widely known regression models and therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. In addition, we define martingale and deviance residuals to detect outliers and evaluate the model assumptions. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.

MSC:
62E10 Characterization and structure theory of statistical distributions
62F10 Point estimation
62N05 Reliability and life testing
Software:
Ox
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