Testing the Ratio of the Coefficients of Variation for the Inverse Gamma Distributions with an Application to Rainfall Dispersion in Thailand
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Abstract
In Thailand, droughts are regular natural disasters that happen nearly every year due to several factors such as precipitation deficiency, human activity, and global warming. Since annual rainfall amounts fit an inverse gamma (IG) distribution, we consider testing annual rainfall dispersion via the ratio of the coefficients of variation (CVs). Herein, we present three statistics for testing the ratio of the CVs of the IG distributions based on the fiducial quantities (FQ) and the Bayesian methods by the Jeffreys and uniform priors. We evaluated their performances by using Monte Carlo simulations conducted under several shape parameter values for the IG distributions based on empirical type I error rates and powers of the tests. The simulation results reveal that the empirical type I error rates of all test statistics were close to the nominal significance level of 0.05 for all situations. In the case of the power of the test, the test statistics based on the Bayesianmethod by the Jeffreys prior performed better than other test statistics for equal sample sizes. In case of unequal sample sizes, the test statistics based on the Bayesian method by the Jeffreys and uniform priors performed well which based on the hypothesized values of ratio of the CVs. Furthermore, the efficacies of the proposed test statistics were illustrated by applying them to annual rainfall dispersion in Buriram and Chaiyaphum, Thailand.
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