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The Birnbaum–Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). Furthermore, the coefficient of variation (CV) is commonly used to analyze variation within a dataset. In some situations, the independent samples are collected from different instruments or laboratories. Consequently, it is of importance to make inference for the common CV. To this end, confidence intervals based on the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), large-sample (LS), Bayesian credible interval (BayCrI), and highest posterior density interval (HPDI) methods are proposed herein to estimate the common CV of several BS distributions. Their performances in terms of their coverage probabilities and average lengths were investigated by using Monte Carlo simulation. The simulation results indicate that the HPDI-based confidence interval outperformed the others in all of the investigated scenarios. Finally, the efficacies of the proposed confidence intervals are illustrated by applying them to real datasets of PM10 (particulate matter ≤ 10 μm) concentrations from three pollution monitoring stations in Chiang Mai, Thailand. [ABSTRACT FROM AUTHOR]

Herein, we present confidence intervals for the variance and difference of variances of Birnbaum-Saunders distributions constructed by using the bootstrap confidence interval (BCI), the generalized confidence interval (GCI), the Bayesian confidence interval (BayCI), and the highest posterior density interval (HPD). The performances of the proposed confidence intervals were investigated in terms of their coverage probabilities and average lengths by running a Monte Carlo simulation. The simulation results reveal that HPD performed the best, even for small sample sizes and/or different values of the shape parameter. To illustrate the efficacy of the proposed confidence intervals, we applied them to datasets of the PM 2.5 concentration in Chiang Mai, Thailand. [ABSTRACT FROM AUTHOR]