Classical and Bayesian Methods for Testing the Ratio of Variances of Delta-Lognormal Distributions

Six test statistics based on classical methods such as the generalized confidence interval (GCI), fiducial GCI (FGCI), and the method of variance estimates recovery (MOVER), as well as Bayesian methods using the highest posterior density (HPD) based on Jeffreys’ prior (HPD-Jef), Jeffreys’ rule prior (HPD-Rul), and the normal-gamma (HPD-NG) prior, for testing the ratio of variances of delta-lognormal distributions are proposed herein. A simulation study was conducted under several ratios of delta-lognormal variances to compare the performances of the proposed test statistics based on their empirical type I error rates and powers of the tests. The simulation results show that the MOVER test statistic performed well in terms of the empirical type I error rate for small sample sizes. In addition, the test statistics based on GCI, FGCI, and HPD-NG can be recommended for large sample sizes. When comparing the powers of the tests, the GCI and FGCI test statistics obtained higher powers than the others for moderate sample sizes while the HPD-NG test statistic achieved the highest power for large sample sizes. Daily rainfall amounts in the lower and upper northern regions of Thailand where the data follow delta-lognormal distributions were applied to illustrate the practical use of the proposed test statistics.