Estimating the Confidence Intervals for the Coefficients of Variation Delta-Gamma Distributions

Abstract

A common application of the coefficient of variation (CV), which is the ratio of the population standard deviation to the population mean, is frequently used to assess quality control and economic processes, among others. The fiducial quantity approach, Bayesian confidence intervals (CIs) using the Jeffreys, uniform, or normal-gamma-beta (NGB) priors, and highest posterior density (HPD) intervals using the Jeffreys, uniform, or NGB priors were used to provide estimators for the CI for the ratio of CV of two delta-gamma distributions. An evaluation of their performance in terms of average length and coverage probability was carried out using Monte Carlo simulations. The results of this study indicate that the HPD using the Jeffreys prior and fiducial quantity methods are the best for estimating the CI for the ratio of the CV of two delta-gamma distributions. Rainfall data from Mae Hong Son province in Thailand was used to illustrate their practicability when analyzing real-life processes.