Wald transformation-based confidence interval for a coefficient of variation of Gamma distribution with applications to PM 2.5 dispersion measurement

Abstract

Accurate estimation of the coefficient of variation (CV) is essential for assessing the variability of environmental pollutants such as fine particulate matter (PM2.5). This study proposes a Wald transformation-based (Wald-TB) confidence interval for the CV of Gamma-distributed data by transforming a Gamma random variable into an approximately normal random variable and subsequently applying the Wald procedure. The performance of the proposed method is compared with the Score, Wald, generalized confidence interval (GCI), and Modified McKay methods. The results show that the proposed Wald-TB interval consistently achieves coverage probabilities close to the nominal 95% confidence level while producing interval widths and relative bias comparable to those of the GCI method and improving upon the conventional Wald interval. Although the GCI method exhibits slightly better overall statistical performance, the proposed Wald-TB approach provides a simple closed-form confidence interval that can be computed directly without simulation. The proposed method is further illustrated using PM2.5 concentration data collected in Hat Yai, Thailand, where it yields confidence intervals comparable to those obtained by existing methods. These findings demonstrate that the Wald-TB interval offers an accurate, computationally efficient, and practically appealing alternative for interval estimation of the coefficient of variation in Gamma-distributed data.