The problem of estimating parameters in a gamma distribution has been widely studied with respect to both theories and applications. In special cases, when the parameter space is bounded, the construction of the confidence interval based on the classical Neyman procedure is unsatisfactory because the information regarding the restriction of the parameter is disregarded. In order to develop the estimator for this issue, the confidence intervals for the coefficient of variation for the case of a gamma distribution were proposed. Extending to two populations, the confidence intervals for the difference and the ratio of coefficients of variation with restricted parameters were presented. Monte Carlo simulations were used to investigate the performance of the proposed estimators. The results showed that the proposed confidence intervals performed better than the compared estimators in terms of expected length, especially when the coefficients of variation were close to the boundary. Additionally, two examples using real data were analyzed to illustrate the findings of the paper.
