Unit-bimodal Birnbaum-Saunders distribution with applications

Abstract

In this paper, we consider a transformation in a random variable which follows a bimodal Birnbaum-Saunders distribution. We propose the unit-bimodal Birnbaum-Saunders (UBBS) distribution and investigate some of its important properties, like cumulative distribution function, moments, survival function and risk function. We apply the UBBS distribution to censored data inflated at zero and one. We used the maximum likelihood approach for parameter estimation and to compare the models. Given the flexibility in UBBS distribution modes, our proposal performs best in beta regression models with zero and/or one excess.

Keywords:

• Censoring
• Maximum likelihood estimation
• Birnbaum-Saunders distribution
• Regression model

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62E15
• 62E20

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Funding

The research of G. Martínez-Flórez was supported by project grant “FCB-03-18” entitled “Distribuciones de probabilidad asimétrica bimodal con soporte positive,” from the Universidad de Córdoba, Colombia. The research of N.M. Olmos was supported by SEMILLERO UA-2022 (Chile).