On a bivariate Birnbaum-Saunders distribution parameterized by its means: features, reliability analysis and application

TL;DR

This paper introduces a new bivariate Birnbaum-Saunders distribution parameterized by means, explores its properties, estimation methods, and demonstrates its application through simulation and real data analysis.

Contribution

It presents the first bivariate Birnbaum-Saunders model with means as parameters, along with estimation techniques and practical applications.

Findings

The model's properties are thoroughly characterized.

Maximum likelihood and modified moment estimators are evaluated.

The model effectively fits real-world positively skewed data.

Abstract

Birnbaum-Saunders models have been widely used to model positively skewed data. In this paper, we introduce a bivariate Birnbaum-Saunders distribution which has the means as parameters. We present some properties of the univariate and bivariate Birnbaum-Saunders models. We discuss the maximum likelihood and modified moment estimation of the model parameters and associated inference. A simulation study is conducted to evaluate the performance of the maximum likelihood and modified moment estimators. The probability coverages of confidence intervals are also discussed. Finally, a real-world data analysis is carried out for illustrating the proposed model.