On a bimodal Birnbaum-Saunders distribution with applications to lifetime data

TL;DR

This paper introduces a new bimodal Birnbaum-Saunders distribution based on the alpha-skew-normal, providing mathematical properties, estimation methods, and demonstrating its superior fit on real lifetime data sets.

Contribution

The paper develops a novel bimodal Birnbaum-Saunders distribution using alpha-skew-normal, with comprehensive properties, estimation techniques, and empirical validation showing improved performance over existing models.

Findings

The new distribution effectively models bimodal lifetime data.

Maximum likelihood estimators perform well in simulations.

The model outperforms existing bimodal Birnbaum-Saunders extensions.

Abstract

The Birnbaum-Saunders distribution is a flexible and useful model which has been used in several fields. In this paper, a new bimodal version of this distribution based on the alpha-skew-normal distribution is established. We discuss some of its mathematical and inferential properties. We consider likelihood-based methods to estimate the model parameters. We carry out a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators. For illustrative purposes, three real data sets are analyzed. The results indicated that the proposed model outperformed some existing models in the literature, in special, a recent bimodal extension of the Birnbaum-Saunders distribution.