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Estimation of the Number of Classes in a Population
Author(s) -
Arnold Barry C.,
Beaver Robert J.
Publication year - 1988
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.4710300404
Subject(s) - mathematics , statistic , statistics , population , interval (graph theory) , sample (material) , simple (philosophy) , sample size determination , point estimation , combinatorics , demography , philosophy , chemistry , epistemology , chromatography , sociology
The problem of estimating M , the number of classes in a population, is formulated as an occupancy problem in which N items are drawn from M urns. Under the assumption of a uniform distribution for the number of classes in the population, the sufficient statistic for M , which is the number of distinct classes observed, does not depend upon the number of repetitions in the sample. Point and interval estimates of M are developed using maximum likelihood and the method of moments. Both techniques give rise to the same basic equation which requires a simple iterative solution. These same techniques are used in the more general situation in which the classes can be further subdivided according to type.