Some Methods of Estimation for the Poisson Binomial Distribution

The Poisson Binomial distribution has been fitted with considerable success to the data on the spread of European corn-borers in field corn (cf. McGuire et al. [3]). One of the problems in fitting this distribution is that of estimating the parameters. The method of the first two moments and that of the first moment and the first frequency have been discussed by Sprott [6]. It is apparent from the tables of efficiency given therein that while these methods have high efficiency in certain regions of the parameter space, the regions are not wide enouigh to include the parameter vectors of most of the populations that arise in practice. The aim of this paper is to discuss a method of estimation which we believe yields estimators with high efficiency in most practical cases. In order to compare this method with the methods mentioned above, tables of efficiency given by Sprott for these methods are calculated to higher accuracy and extended to include larger values of the parameters. All the computations were done on an electroniic computer IBM 650. A method for estimating the parameters in the Poisson Binomial distribution based on maximum likelihood was presented by Sprott [6] and was simplified by Shumway and Guirland [5]. In [5], a table is provided which simplifies the computations when the parameter n (to be described below) is equal to 2. The method-even in its simplified form-leads to iteration in an equation which involves as many terms as there are nonl-zero frequencies and hence may not be as simple and