Estimation Methods for the Coefficient of Variation of the Three-Parameter Lognormal Distribution: Their Application to Wind Speed Data Indicating Soil Erosion Effects

Highly right-skewed data can often be modeled by using the three-parameter lognormal distribution. Meanwhile, the performances of extant confidence interval estimates are poor when the variance is large. Herein, methods to estimate the confidence interval for the coefficient of variation of the three-parameter lognormal distribution using the likelihood-based, generalized confidence interval, and method of variance estimates recovery methods are presented. The results of a numerical simulation study reveal that the likelihood-based confidence interval estimate performed well in terms of the actual coverage percentage and average length, even with a large coefficient of variation. The methods’ applicability is demonstrated through their application to wind speed data from Chiang Mai, Thailand, aiming to indicate soil erosion effects.