Estimating purchase frequency distributions with incomplete data

A procedure is developed for estimating the parameters of a a purchase frequency distribution law for each stratum of stratified random consumer sample when both nonresponsive trials and inaccurate observations occur and one or more aggregate statistics are given. Explicit use is made of the information given by the incidence of nonresponsive trials. Simplifying assumptions are made concerning the nature of the inaccurate observations. The model is shown to be equivalent to a linear programming problem. An application of the model to projecting market survey results to the total population (total market) size is presented. Solved examples and avenues of generalization are included.