Statistical Methods by a Reparameterization of the Coefficient of Variation for a Three-Parameter Lognormal Model: An Application to Thailand Rainfall Kinetic Energy Data

In the study, a crucial research gap concerning the estimation of the coefficient of variation in an asymmetric distribution was addressed, specifically focusing on the three-parameter lognormal (3PLN) model, which exhibits large variation. The purpose of this research was to determine the effectiveness of four statistical approaches: likelihood-based, parametric bootstrap, profile likelihood, and Bayesian inference in formulating confidence intervals for reparameterizing the coefficient of variation (CV) within the 3PLN model. To evaluate the performance of the confidence intervals, we utilize specific performance measures such as the coverage rate and mean length. The results of our simulation study provide insights into how the profile likelihood method performs in estimating the CV, showing its effectiveness compared to alternative methods, particularly in ensuring accurate coverage rates. Nevertheless, when utilizing Adam’s optimization algorithm to derive point estimates, the Bayesian approach stands out as a dependable option for establishing confidence intervals, especially when dealing with a wide range of variances, from small to large. To demonstrate the practical application of our research, we utilize all proposed confidence intervals in estimating rainfall kinetic energy data. This real-world application serves as validation and showcases the utility of confidence intervals in practical scenarios.