Abstract
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.
Highlights
When several random variables comprise non-negative values, their dissemination will fit neither a normal nor other symmetrical distributions, and so asymmetrical distributions must be considered instead
We propose confidence intervals for these two scenarios by applying the concepts of generalized confidence interval (GCI), the bootstrap confidence interval (BCI), the Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval
We evaluated the performances of GCI, bootstrapped confidence interval (BCI), BayCI, and the HPD interval by measuring their coverage probabilities and average lengths based on 5000 independently generated replications, with 5000 pivotal quantities for GCI, B = 500 for BCI, and N = 5000 for BayCI and the HPD interval
Summary
When several random variables comprise non-negative values, their dissemination will fit neither a normal nor other symmetrical distributions, and so asymmetrical distributions must be considered instead. Despite the diverse theoretical and methodological developments for constructing confidence intervals from the functions of parameters of BS distributions, there have not yet been any studies on the single CV and the difference between the CVs of BS distributions. To fill this gap, we propose confidence intervals for these two scenarios by applying the concepts of GCI, the bootstrap confidence interval (BCI), the Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
