Testing the Coefficient of Variation for the Inverse Gamma Distribution: A Case Study of the Annual Rainfall Amounts in Lampang, Thailand

Abstract

Two test statistics for testing the coefficient of variation in an inverse gamma distribution were proposed in this study. The proposed test statistics were based on the score and Wald methods. An evaluation of the performance of the proposed test statistics using Monte Carlo simulations was conducted under several shape parameter values in an inverse gamma distribution. The performances of the test statistics were compared based on the empirical type I error rates and the powers of the tests. The simulation results revealed that the test statistics based on the Wald method performed better than the test statistics based on the score method in terms of the attained nominal significance level and is thus recommended for analysis in similar scenarios. The efficacies of the proposed test statistics were also illustrated by applying them to annual rainfall amounts in Lampang, Thailand.