Simplified techniques for estimating parameters of some generalized Poisson distributions

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Abstract
Three similar procedures for parameter estimation are investigated for the Negative Binomial, Neyman Type A, Poisson Pascal, and Poisson Binomial distributions. These procedures are based on h-functions, h-functions combined with a-function of the zero frequency, and l-functions. The estimators so obtained are of the same form as weighted least squares. In comparing the estimation procedures for a given number of functions, use of (ho, h1,…, hs, ai) generally results in the highest asymptotic relative efficiency. In some parts of the parameter space of the Poisson Binomial distribution, the l-functions have the highest efficiency. The use of two or three h-functions together with an a-function is very effective and yields fittings that rival maximum likelihood. A graphical procedure based on the h-and l-functions for helping to choose among the four distributions is also presented. In making such a choice in the absence of preliminary information about the relevant underlying distribution this graphical procedure has some merit.

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