On a restricted occupancy model and its applications

✍ Scribed by Dr. Ch. A. Charalambides

• Publisher: John Wiley and Sons
• Year: 1981
• Tongue: English
• Weight: 480 KB
• Volume: 23
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710230609

✦ Synopsis

Abstract

With the multivariate hypergeometric distribution as a background certain occupancy distributions useful in practical applications are derived. More specifically it is assumed that a sample of n individuals is drawn from a population consisting of m types with r individuals in each type, (i) without replacement and (ii) by returning the selected individual in the population and with it another individual of the same type. The distributions of the number Z of distinct types observed in the sample are obtained in both cases in terms of the numbers. Assuming, in addition to the m equiprobable types of individuals, the existence of a control type, say, with s individuals, the joint distribution of the number U of distinct types observed in the sample and the number V of individuals of the control type present in the sample is obtained in terms of the numbers C(n, k, r) and the marginal distribution of U in terms of the Gould‐Hopper numbers. Using these distributions minimum variance unbiased estimators of the number m of types are derived. Moreover small sample tests based on the zero frequency are constructed.