Weighted Lindley regression model with varying precision: estimation, modeling and its diagnostics

Abstract

The two-parameter weighted Lindley distribution has become much popular due to its simplicity, attractive properties, and flexibility to fit data when compared with similar generalizations of the exponential model, such as gamma and Weibull, among others. In this paper, we introduce a regression model based on a weighted Lindley distribution, which is reparameterized in terms of mean and precision parameters. In this model, both the mean and precision parameters vary with the explanatory variable values and general link functions are used in order to account for these relationships. We developed and implemented local influence diagnostics to identify potential influential observations. Hessian and Fisher information matrices are computed on the closed-form as well as their inverses. Classical inference based on the maximum likelihood method is presented. Extensive Monte Carlo simulation studies are carried out for a special case of the regression model in order to verify the asymptotic properties of the maximum likelihood estimators. Finally, the usefulness of the proposed model is illustrated through an empirical analysis.