Vol.:(0123456789) Journal of Statistical Theory and Practice (2019) 13:27 https://doi.org/10.1007/s42519-018-0026-3 1 3 ORIGINAL ARTICLE Log‑Burr XII Gamma–Weibull Regression Model with Random Efects and Censored Data Elizabeth M. Hashimoto 1  · Giovana O. Silva 2  · Edwin M. M. Ortega 3  · Gauss M. Cordeiro 4 © Grace Scientific Publishing 2018 Abstract It may happen in some applications that the assumption of independence of sur- vival times does not hold. Thus, we propose a new log-Burr XII regression model with log-gamma–Weibull distributions for the random efects. The maximum like- lihood method is used to estimate the model parameters based on the Gauss–Her- mite numerical integration technique. For diferent parameter settings, sample sizes, censoring percentages and correlated data, various simulations are performed. Some global-infuence measurements are also investigated. In order to assess the robust- ness of the maximum likelihood estimators, we evaluate local infuence on the estimates of the parameters under diferent perturbation schemes. We illustrate the importance of the new model by means of a real data set in analysis of experiments. Keywords Censored data · Log-gamma–Weibull distribution · Random efect · Regression model 1 Introduction In regression models for survival analysis, the usual assumption that the survival times of distinct elements are independent may not be valid in some applications. Sometimes the elements observed form a group, and thus, the survival times within each group might not be mutually independent. This is the case, for example, of data observed about people of the same family or animals of the same litter. Besides * Edwin M. M. Ortega edwin@usp.br 1 Departamento Acadêmico de Matemática, UTFPR, Curitiba, Brazil 2 Departamento de Estatística, UFBA, Salvador, Brazil 3 Departamento de Ciências Exatas, ESALQ - USP, Av. Pádua Dias 11, Caixa Postal 9, 13418-900 Piracicaba, São Paulo, Brazil 4 Departamento de Estatística, UFPE, Recife, Brazil