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Estimating the uncertainty associated with a variable in a finite population. (English) Zbl 0655.62006

This paper is concerned with the problem of estimating the uncertainty associated with a variable in a finite population. The study of this problem leads to the following conclusion: The classical measure of uncertainty, Shannon’s entropy, is not suitable for sampling from finite populations; nevertheless, by using the entropy of order \(\beta =2\), proposed by J. Havrda and F. Charvát [Kybernetika 3, 30–35 (1967; Zbl 0178.22401)] one can define an unbiased estimator of the uncertainty associated with the variable in both, the sampling with replacement and the sampling without replacement. This conclusion will be illustrated by an example.
Reviewer: R. Perez

MSC:

62D05 Sampling theory, sample surveys
62B10 Statistical aspects of information-theoretic topics

Citations:

Zbl 0178.22401
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References:

[1] Devijver P. A., I.E.E.E. Trans, on Computers, C.23 (1974)
[2] Azorin F., Proc. F.I.S.A.L.-83, Palma de Mallorca pp 37– (1983)
[3] DOI: 10.1016/0096-3003(77)90008-X · Zbl 0403.62018
[4] DOI: 10.1016/S0022-5193(74)80057-3
[5] DOI: 10.1038/163688a0 · Zbl 0032.03902
[6] Pielou E. C., An introduction to Mathematical Diversity (1969) · Zbl 0259.92001
[7] DOI: 10.1016/S0019-9958(70)80040-7 · Zbl 0205.46901
[8] Gil M. A., Trab. de Est. e Inv. Oper. 32 pp 3– (1981)
[9] DOI: 10.1016/S0019-9958(78)90659-9 · Zbl 0393.94011
[10] Gil M. A., R.A.I.R.O. Rech. Opér. 16 pp 319– (1982)
[11] Gil M. A., Statistica. Anno (1) pp 21– (1982)
[12] Zagier D., Discussion paper No. 108, Projectgruppe ”Theoretische inodelle (1983)
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