Bayesian Estimation for the Coefficients of Variation of Birnbaum-Saunders Distributions

The Birnbaum-Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an important descriptive statistic for explaining variation within a dataset, has not previously been used for statistical inference on a BS distribution. The aim of this study is to present four methods for constructing confidence intervals for the CV, and the difference between the CVs of BS distributions. The proposed methods are based on the generalized confidence interval (GCI), a bootstrapped confidence interval (BCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval. A Monte Carlo simulation study was conducted to evaluate their performances in terms of coverage probability and average length. The results indicate that the HPD interval was the best-performing method overall. PM 2.5 concentration data for Chiang Mai, Thailand, collected in March and April 2019, were used to illustrate the efficacies of the proposed methods, the results of which were in good agreement with the simulation study findings.

Automated summary

This study introduces four methods for constructing confidence intervals for the coefficient of variation (CV) and the difference between CVs of Birnbaum-Saunders (BS) distributions. A Monte Carlo simulation shows that the highest posterior density (HPD) interval performs best overall. The proposed methods were validated using PM 2.5 concentration data for Chiang Mai, Thailand in March and April 2019, with results consistent with the simulation findings.