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

Perez, R.; Gil, M. A.; Gil, P.

Kybernetes 15, 251-256 (1986).

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

Keywords:

finite population; measure of uncertainty; Shannon’s entropy; unbiased estimator of the uncertainty; sampling with replacement; sampling without replacement

Citations:

Zbl 0178.22401

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