Confidence Intervals of the Inverse of Coefficient of Variation of Delta-Gamma Distribution

The inverse of the coefficient of variation (ICV), otherwise known as the signal to-noise ratio, is the ratio of the population standard deviation to the population mean. It has often been used in the fields of finance and image processing, among others. In this study, various methods were applied to estimate the confidence intervals (CIs) for the difference between and the ratio of the ICVs of two delta-gamma distributions. The fiducial quantity method, Bayesian CI estimates based on the Jeffreys, uniform, or normal-gamma-beta (NGB) prior, and highest posterior density (HPD) intervals based on the Jeffreys, uniform, or NGB priors were used in this endeavor. A Monte Carlo simulation study was conducted to assess the performances of the proposed CI estimation methods in terms of their coverage probabilities and average lengths. The results indicate that the HPD interval based on the NGB prior or the Jeffreys prior performed well for a small probability of the samples containing zero observations (delta) whereas the fiducial quantity method performed well for large values of d. Furthermore, we demonstrate the practicability of the proposed methods using rainfall data from Lampang province, Thailand.