Testing the annual rainfall dispersion in Chaiyaphum, Thailand, by using confidence intervals for the coefficient of variation of an inverse gamma distribution

In Thailand, droughts are regular natural disasters that happen nearly every year due to several factors such as precipitation deficiency, human activity, and the global warming. Since annual rainfall amount fits an inverse gamma (IG) distribution, we wanted to try testing annual rainfall dispersion via the coefficient of variation (CV). Herein, we propose two statistics for testing the CV of an IG distribution based on the Score and Wald methods. We evaluated their performances by means of the Monte Carlo simulations conducted under several shape parameter values for an IG distribution based on empirical type I error rates and powers of the tests. The simulation results reveal that the Wald-method test statistic performed better than the Score-method one in terms of the attained nominal significance level, and is thus recommended for analysis in similar scenarios. Furthermore, the efficacy of the proposed test statistics was illustrated by applying them to the annual rainfall amounts in Chaiyaphum, Thailand.