Abstract

In this paper, we propose and derive a Birnbaum-Saunders distribution to model bimodal data. This new distribution is obtained using the product of the standard Birnbaum-Saunders distribution and a polynomial function of the fourth degree. We study the mathematical and statistical properties of the bimodal Birnbaum-Saunders distribution, including probabilistic features and moments. Inference on its parameters is conducted using the estimation methods of moments and maximum likelihood. Based on the acceptance-rejection criterion, an algorithm is proposed to generate values of a random variable that follows the new bimodal Birnbaum-Saunders distribution. We carry out a simulation study using the Monte Carlo method to assess the statistical performance of the parameter estimators. Illustrations with real-world data sets from environmental and medical sciences are provided to show applications that can be of potential use in real problems.