Models for Cataloguing Problems

Abstract

Suppose that the members of a population fall into an unknown number of classes of various sizes. A random sample of $N$ observations is taken and from the information in the sample must be estimated the parameters of the population; roughly speaking these are the number of classes of a given size. This description is deliberately vague because there are two models available in the literature for this problem. Good (1953), Good and Toulmin (1956), Harris (1959), and Trybula (1959) use an infinite population and investigate estimators for useful functions of the population parameters. Examples of applications are given. Goodman (1949) uses a finite population and obtains rather more restricted results. Des Raj (1961) also treats a very special case of this model. Such problems have been called cataloguing problems, see Harris (1959), which is the reason for the title. It is the object of this paper to show that the second model, that with finite population, is more suitable for these problems, and to extend the results of Goodman to match those available for the model with infinite population. The unbiased estimators obtained would be modified for practical use, and the main contribution of the paper is thought to lie in the simplification of the theory connected with the problem.