Interval Estimation for the Common Coefficient of Variation of Gamma Distributions

Abstract

The method of variance of estimate recovery (MOVER) has been widely used to construct the confidence interval for the function of parameters. This method is based on estimating the variance of the related estimators and recovering them to the confidence interval for the parameter of interest. However, only confidence intervals for one- or two-sample in the gamma distribution have been reported, whereas in many research areas, more than two samples must be studied.  In this paper, we therefore introduce three confidence intervals for the common coefficient of variation (CV) of multiple gamma distributions. The traditional MOVER is extended as the adjusted MOVER. The first two proposed confidence intervals are constructed using the adjusted MOVER with existing confidence limits obtained from the score and Wald methods. The third is formulated using normal approximation. The performance of these estimators was investigated using simulations. The results showed that the confidence interval derived by the adjusted MOVER with the Wald method satisfied the criteria for coverage probability in the general cases. Two real-world datasets were analyzed to confirm the practical application of these estimators.