Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution

Inference based on popular maximum-likelihood estimators (MLEs) method often provide bias estimates of order O(n-1)$ \mathcal {O}(n^{-1})$. Such bias may significantly affect the accuracy of estimates. This observation motivates us to adopt some bias-corrected technique to reduce the bias of the MLE from order O(n-1)$ \mathcal {O}(n^{-1})$ to order O(n-2)$ \mathcal {O}(n^{-2})$. In this paper, we consider the unit-gamma distribution which has some properties similar to the Beta distribution. This distribution is obtained by transforming a Gamma random variable but it has not been widely explored in the literature. We adopt a “corrective” approach to derive second-order bias corrections of the MLEs of its parameters. Additionally, we also consider the parametric Bootstrap bias correction. Monte Carlo simulations are conducted to investigate the performance of proposed estimators. Our results revels the bias corrections improve the accuracy of estimates. Finally, two real data examples are discussed to illustrate the applicability of the unit-Gamma distribution.