Some Methods of Estimation for the Poisson Binomial Distribution

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Abstract
The methods of estimating the parameters of the Poisson Binomial distribution using (i) the first two moments and (ii) the first moment and the first frequency have been discussed by Sprott in Biometrics 1958 as alternatives to maximum likelihood estimates. It is apparent from the table of efficiency given therein that while those methods have high efficiency in certain regions of the parameter space, the regions are not wide enough to include the parameter vectors of most of the populations that arise in practice. In this paper, the distribution is regarded as a two parameter family and a method of estimating the parameters by minimizing a certain quadratic form in three functions of parameters is discussed. The particular case in which the functions used are the first two factorial cumulants and the logarithm of the zero frequency is considered and the asymptotic efficiency of the estimators is tabulated. On the basis of these tables, it is believed that this method can be used as a reasonable substitute for the highly complex efficiency methods. The simplicity of equations for estimation relative to the maximum likelihood equations is noticeable.