On a nonlinear Birnbaum–Saunders model based on a bivariate construction and its characteristics

Abstract

The Birnbaum-Saunders (BS) distribution is an asymmetric probability model that is receiving considerable attention. In this article, we propose a methodology based on a new class of BS models generated from the Student-t distribution. We obtain a recurrence relationship for a BS distribution based on a nonlinear skew–t distribution. Model parameters estimators are obtained by means of the maximum likelihood method, which are evaluated by Monte Carlo simulations. We illustrate the obtained results by analyzing two real data sets. These data analyses allow the adequacy of the proposed model to be shown and discussed by applying model selection tools.

Keywords:

• Data analysis
• Elliptically contoured distributions
• Likelihood and Monte Carlo methods
• Linear and nonlinear skew–elliptic distributions

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60E05
• Secondary 62–07

Acknowledgments

The authors thank the Editors and anonymous referees for their constructive comments on an earlier version of this article.

Additional information

Funding

Mohsen Khosravi and Ahad Jamalizadeh thank the Mahani Mathematical Research Center (Kerman, Iran) for its support. Victor Leiva and Emilio Porcu were supported by FONDECYT 1120879 and 1130647 grants of the Comisión Nacional de Investigación Científica y Tecnológica from the Chilean government.