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Associated LAH Numbers, Factorial Series Distributions and Unbiased Estimation of a Size Parameter
Author(s) -
Berg S.
Publication year - 1987
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.4710290209
Subject(s) - mathematics , statistics , estimator , sample size determination , series (stratigraphy) , parametric statistics , sampling (signal processing) , efficiency , sampling scheme , population , factorial , best linear unbiased prediction , sequential estimation , selection (genetic algorithm) , mathematical analysis , computer science , sociology , computer vision , biology , paleontology , demography , filter (signal processing) , artificial intelligence
A finite population consists of kN individuals of N different categories with k individuals each. It is required to estimate the unknown parameter N , the number of different classes in the population. A sequential sampling scheme is considered in which individuals are sampled until a preassigned number of repetitions of already observed categories occur in the sample. Corresponding fixed sample size schemes were considered by Charalambides (1981). The sequential sampling scheme has the advantage of always allowing unbiased estimation of the size parameter N . It is shown that relative to Charalambides' fixed sample size scheme only minor adjustments are required to account for the sequential scheme. In particular, MVU estimators of parametric functions are expressible in terms of the C ‐numbers introduced by Charalambides.