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.

Keywords:

• GAMLSS
• Local influence
• Maximum likelihood estimators
• Randomized quantile residuals
• Weighted Lindley distribution

Acknowledgments

The authors are very grateful to the Editorial Board and the anonymous referees for their helpful and useful comments that improved the manuscript. Alex Mota and Milton Miranda Neto acknowledge the support of the Coordenação de Aperfeioamento de Pessoal de Nível Superior (CAPES)—Finance Code 001. Jeremias Leão is supported by the Brazilian agency FAPEAM. Francisco Louzada is supported by the Brazilian agencies CNPq (grant number 301976/2017-1) and FAPESP (grant number 2013/07375-0).

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that support the findings of this study are available at http://stats.oecd.org/Index.aspx?DataSetCode=BLI.