Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored - Gianfelice, Paulo Roberto de Lima [UNESP] (2020)
This work presents a study of probabilistic modeling, with applications to survival analysis, based on a probabilistic model called Exponential Geometric (EG), which o ers great exibility for the statistical estimation of its parameters based on samples of life time data complete and censored. In this study, the concepts of estimators and lifetime data are explored under random censorship in two cases of extensions of the EG model: the Extended Geometric Exponential (EEG) and the Generalized Extreme Geometric Exponential (GE2). The work still considers, exclusively for the EEG model, the approach of the presence of covariates indexed in the rate parameter as a second source of variation to add even more exibility to the model, as well as, exclusively for the GE2 model, a analysis of the convergence, hitherto ignored, it is proposed for its moments. The statistical inference approach is performed for these extensions in order to expose (in the classical context) their maximum likelihood estimators and asymptotic con dence intervals, and (in the bayesian context) their a priori and a posteriori distributions, both cases to estimate their parameters under random censorship, and covariates in the case of EEG. In this work, bayesian estimators are developed with the assumptions that the prioris are vague, follow a Gamma distribution and are independent between the unknown parameters. The results of this work are regarded from a detailed study of statistical simulation applied to compare the estimation procedures approached under the pretext of evaluating these estimators based on the 95% coverage probability, mean square error, mean bias and the mean interval amplitude. At the end of each extension's approach, an application with real data is also presented to highlight the reach and particularities of the extended model addressed.