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On a restricted occupancy model and its applications
Author(s) -
Charalambides Ch. A.
Publication year - 1981
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710230609
Subject(s) - mathematics , hypergeometric distribution , statistics , sample (material) , type (biology) , population , estimator , joint probability distribution , sample size determination , distribution (mathematics) , occupancy , variance (accounting) , multivariate statistics , combinatorics , mathematical analysis , demography , ecology , chemistry , accounting , chromatography , sociology , business , biology
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.