Simultaneous confidence intervals for all pairwise differences of coefficients of variation of zero-inflated Birnbaum–Saunders distributions

Usanee Janthasuwan; Suparat Niwitpong; Sa-Aat Niwitpong; Usanee Janthasuwan; Suparat Niwitpong; Sa-Aat Niwitpong

doi:10.3934/math.2026162

AIMS Mathematics

2026, Volume 11, Issue 2: 4043-4067. doi: 10.3934/math.2026162

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Simultaneous confidence intervals for all pairwise differences of coefficients of variation of zero-inflated Birnbaum–Saunders distributions

Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 06 November 2025 Revised: 03 February 2026 Accepted: 05 February 2026 Published: 09 February 2026
MSC : 62F25, 62P12

The data used for the analysis were collected from multiple regions or years. Evaluating each region or year separately may be insufficient for drawing comprehensive inferences and may fail to reveal statistically significant differences. To ensure the reliability of the analysis and to enable overall conclusions, it is necessary to apply a statistical method known as simultaneous confidence intervals. This technique enables the simultaneous construction of confidence intervals for multiple parameters. Therefore, we proposed and evaluated methods for constructing simultaneous confidence intervals for all pairwise differences between the coefficients of variation in zero-inflated Birnbaum-Saunders distributions. The methods utilized for constructing simultaneous confidence intervals comprise the generalized confidence interval (GCI), the bootstrap confidence interval (BCI), the method of variance estimates recovery (MOVER), the MOVER based on GCI, the MOVER based on BCI, the Bayesian credible interval, and the highest posterior density interval (HPD). Monte Carlo simulations were employed to evaluate the performance of each method, which involved the assessment of coverage probabilities and average widths under a set of parameter configurations and sample sizes. The generalized confidence interval method was the most efficient overall, as indicated by the simulation results. Finally, all proposed methods were applied to real-world wind speed data to examine their practical applicability and to demonstrate the consistency of the results between the simulation study and real-world applications.
- average width,
- coefficient of variation,
- coverage probability,
- simultaneous confidence interval,
- zero-inflated Birnbaum-Saunders
Citation: Usanee Janthasuwan, Suparat Niwitpong, Sa-Aat Niwitpong. Simultaneous confidence intervals for all pairwise differences of coefficients of variation of zero-inflated Birnbaum–Saunders distributions[J]. AIMS Mathematics, 2026, 11(2): 4043-4067. doi: 10.3934/math.2026162

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Abstract

The data used for the analysis were collected from multiple regions or years. Evaluating each region or year separately may be insufficient for drawing comprehensive inferences and may fail to reveal statistically significant differences. To ensure the reliability of the analysis and to enable overall conclusions, it is necessary to apply a statistical method known as simultaneous confidence intervals. This technique enables the simultaneous construction of confidence intervals for multiple parameters. Therefore, we proposed and evaluated methods for constructing simultaneous confidence intervals for all pairwise differences between the coefficients of variation in zero-inflated Birnbaum-Saunders distributions. The methods utilized for constructing simultaneous confidence intervals comprise the generalized confidence interval (GCI), the bootstrap confidence interval (BCI), the method of variance estimates recovery (MOVER), the MOVER based on GCI, the MOVER based on BCI, the Bayesian credible interval, and the highest posterior density interval (HPD). Monte Carlo simulations were employed to evaluate the performance of each method, which involved the assessment of coverage probabilities and average widths under a set of parameter configurations and sample sizes. The generalized confidence interval method was the most efficient overall, as indicated by the simulation results. Finally, all proposed methods were applied to real-world wind speed data to examine their practical applicability and to demonstrate the consistency of the results between the simulation study and real-world applications.

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