Confidence intervals for the variance and difference of variances of Birnbaum-Saunders distributions

Abstract

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.

Keywords:

• Birnbaum-Saunders distributions
• variance
• bootstrap
• generalized confidence intervals
• Bayesian confidence interval
• the highest posterior density interval

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author is grateful for funding from the Science Achievement Scholarship of Thailand (SAST). This research received financial support from the National Science, Research, and Innovation Fund (NSRF), and King Mongkut's University of Technology North Bangkok (Grant No. KMUTNB-FF-65-23).