Bayesian Simultaneous Credible Intervals for the Differences of Coefficients of Variation of Weibull Distributions with Application to Wind Speed Data in Thailand

Abstract

The Weibull distribution serves as a versatile tool for modelling various types of data, including reliability analysis, failure rates, survival analysis, and extreme value analysis. Specifically, in weather forecasting, the Weibull distribution is frequently used to represent variables such as wind speed. To examine differences in wind speed dispersion across different areas, the coefficient of variation proves optimal. However, when comparing variations across multiple areas simultaneously, the focus shifts to simultaneous confidence intervals (SCIs). Therefore, this paper focuses on the problem of constructing the SCIs for the differences of coefficients of variation derived from Weibull distributions. The proposed methods in this study are Bayesian approaches that utilize gamma and uniform prior distributions, namely the generalized confidence interval (GCI) and the method of variance estimate recovery (MOVER) based on the Hendricks and Robey interval. To assess the performance of these methods, their coverage probability, expected length, and standard errors were evaluated through a simulation study. The simulation results show that the Bayesian credible interval based on the gamma prior performs satisfactorily in most cases. Finally, to illustrate the SCIs, we present an example concerning wind speed dispersion data in Southern Thailand.