Estimating parameters of the gamma distribution easily and efficiently

Abstract

Being an important probability distribution with moderate skewness, the two-parameter gamma distribution is widely used in statistics. However, the maximum likelihood estimators (MLEs) of its parameters do not have closed forms, making them difficult to be implemented in applications. Moreover, the MLE of its shape parameter has low estimation efficiency due to its considerable bias. Thus, many other estimators have been investigated in the literature. We propose an easy computation of the MLEs in this article, where the MLE of the shape parameter is modified to be highly efficient and significantly better than most of existing estimators.