Modeling Air Pollution Data Using a Generalized Birnbaum-Saunders Distribution with Different Estimation Procedures

As the detrimental impact of air pollution becomes more prevalent; it is crucial to accurately model the distribution of air contamination levels. In practice, the Birnbaum-Saunders distribution is a well-known lifetime model for modeling positively skewed phenomena. Due to its relationship to the normal distribution and other desirable properties, different generalizations for the Birnbaum-Saunders distribution have been extensively studied to improve its flexibility. This article discusses inferential procedures of a specific generalization developed previously but has not received much consideration regarding this specific research area. The considered generalization has an extra shape parameter, known as Type-II generalized Birnbaum-Saunders distribution. The generalized family is more flexible than the Birnbaum-Saunders classical model, as it shares similar properties and can display both unimodality and bimodality. Eight frequentist estimation procedures are considered in this article, including the maximum likelihood and the maximum product of spacing estimation, several regression-based estimations, and goodness-of-fit estimations. Monte Carlo simulations are performed to investigate the estimation efficiency of the methods under various combinations of shape parameters, some conclusions are presented. Furthermore, air pollution concentration data are analyzed using the considered methods to illustrate their practical application. Overall, the analysis results favor the least-squares estimators according to the goodness-of-fit criteria.