Confidence intervals for the difference between coefficients of variation of zero-inflated gamma distributions

Abstract

The problem of constructing confidence intervals (CIs) for the difference between coefficients of variation of two zero-inflated gamma distributions was considered. As gamma distribution does not have closed form maximum likelihood estimators, the parameters of gamma distribution have to be estimated numerically. To this end, we proposed here four different generalized confidence intervals (GCIs) based on fiducial inference, Box-Cox transformation, parametric bootstrap and the method of variance of estimates recovery (MOVER). Performances of the four GCIs were evaluated and compared via extensive simulation. The simulation results showed that all four methods returned satisfactory results according to coverage probabilities, even for the setting of small sample sizes.

Keywords

• confidence interval
• zero-inflated gamma distribution
• coefficient of variation
• rainfall data