ESTIMATING THE UNCERTAINTY ASSOCIATED WITH A VARIABLE IN A FINITE POPULATION

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 ? = 2, proposed by Havrda and Charvat, 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.