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This paper presents a new table and some approximating polynomials especially designed to facilitate maximum likelihood estimation of the parameters of the gamma distribution, and also applicable to the a-parameter Type V; it discusses methods of computing the sampling variances of the likelihood estimators; it illustrates the use of the tables in a numerical example; it mentions applications to the Erlang distribution and difficulties of application to the general Type III. Finally it inquires when the numbers extracted from the tables are maximum likelihood estimates, and what they are estimates of.
Greenwood et al. (Mon,) studied this question.