Simultaneous Confidence Intervals for All Differences of Coefficients of Variation of Normal Distributions with an Application to PM2.5 Dispersion

Abstract

This paper considers the problem of constructing simultaneous confidence intervals (SCIs) for all pairwise differences of coefficients of variation from several normal distributions. The proposed approaches are based on the generalized confidence interval (GCI) approach, the method of variance estimates recovery (MOVER) approach, and the computational approach. The performances of these approaches, using the biased estimator of the coefficient of variation, are compared with the performances of those approaches using the shrinkage estimator. A simulation study based comparison of these SCIs in terms of the coverage probability, average length, and standard error. The simulation results indicated that the GCI approach and the MOVER approach can provide the SCIs with satisfying coverage probabilities regardless of sample sizes. Furthermore, the performances of the biased estimator are better than the performances of the shrinkage estimator. Finally, an application to PM2.5 dispersion in the Northern Thailand is given to illustrate the proposed simultaneous confidence intervals.