Parameter estimation for the beta distribution

Moment estimators, based on the first two sample moments, for the two index parameters of the beta density (known end-points) are studied. Four moments of these estimators are set up using Computer Oriented Extended Taylor Series (COETS) to 60 terms followed by rational fraction approximations. These indicate, over a limited parameter space, that allowing for simplicity of calculation and other characteristics they are preferable to maximum likelihood estimators.