Efficient closed-form maximum a posteriori estimators for the gamma distribution

We proposed a new class of maximum a posteriori estimators for the parameters of the Gamma distribution. These estimators have simple closed-form expressions and can be rewritten as a bias-corrected maximum likelihood estimators presented by Ye and Chen [Closed-form estimators for the gamma distribution derived from likelihood equations. Am Statist. 2017;71(2):177-181]. A simulation study was carried out to compare different estimation procedures. Numerical results revels that our new estimation scheme outperforms the existing closed-form estimators and produces extremely efficient estimates for both parameters, even for small sample sizes.