Estimating the Parameters of a Convolution by Maximum Likelihood

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Abstract
In the present age of computer sophistication, computational difficulty is no longer a justification for seeking alternative and inefficient estimation procedures in place of maximum likelihood estimation, particularly when there are only two or three parameters to be estimated. Convolution densities are an example where this has occurred. It is shown that in a large class of such densities, the maximum likelihood equations can be reduced by one. Thus for a two-parameter family, only a single equation need be solved iteratively. The required formulas are derived. The problem of basing inferences on the resulting maximum likelihood estimates is briefly discussed.

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