Modified goodness-of-fit type test for censored validation under a new Burr type XII distribution with different methods of estimation and regression modeling
Mohamed Ibrahim, Emrah Altun, Hafida Goual, Haitham M. Yousof
Abstract
We proposed a new version of the Burr type XII (BXII) model. Some of its properties are mathematically derived. Different non-Bayesian estimation methods are considered. Numerical simulation studies are performed for assessing their performance. We constructed a modied Nikulin-Rao-Robson chi-square goodness-of-t type test for the new model. This modied test takes into its account both unknown parameters and censorship. A numerical simulation study for validation is performed and we ended with two applications on real data related to cancer data that conrm the results obtained. Moreover, we introduced a new log-location regression model based on the new model. The martingale and modied deviance residual analysis are dened and applied to detect outliers and evaluate the model assumptions.To prove the importance of new regression model, we use the HIV+ data set. For comparing the competitive models, a medical data set related to acute bone cancer employed to compare the competitive models.