An Exponentiated Skew-Elliptic Nonlinear Extension to the Log–Linear Birnbaum–Saunders Model with Diagnostic and Residual Analysis

In this paper, we propose a nonlinear regression model with exponentiated skew-elliptical errors distributed, which can be fitted to datasets high levels of asymmetry and kurtosis. Maximum likelihood estimation procedures in finite samples are discussed the information matrix is deduced. We carried out diagnosis influence for model. To analyze sensitivity maximum estimators model’s parameters small perturbations distribution assumptions parameter estimation, studied perturbation schemes, case weight, explanatory response variables perturbations; also residual analysis deviance components. Simulation studies were performed assess some properties estimators, showing good performance proposed procedure samples. Finally, an application real dataset presented.