A new useful four-parameter extension of the Gumbel distribution: Properties, regression model and applications using the GAMLSS framework

ABSTRACT

In this paper we introduce a flexible extension of the Gumbel distribution called the odd log-logistic exponentiated Gumbel distribution. The new model was implemented in GAMLSS package of R software and a brief tutorial on how to use this package is presented throughout the paper. We provide a comprehensive treatment of its general mathematical properties. Further, we propose a new extended regression model considering four regression structures. We discuss estimation methods based on censored and uncensored data. Two simulation studies are presented and four real data sets are applied to illustrating the usefulness of the new model.

KEYWORDS:

• GAMLSS
• Gumbel distribution
• Maximum likelihood estimation
• Regression model
• Residual analysis

MATHEMATICS SUBJECT CLASSIFICATION:

• 47N30
• 97K70
• 97K80

Acknowledgments

The second author acknowledges the financial support of the “Ciência sem Fronteiras” program of CNPq (Brazil) under the process number 200574/2015-9.