An Entropy Estimator of Population Variability in Nominal Data

Mickie Vanhoy
University of Central Oklahoma

Entropy is an established measure of variability in nominal data. The present paper addresses the problem of directly estimating population entropy from an empirical sample. Thirty artificial, nominal, population distributions were subjected to Monte Carlo analysis. Comparison of sample entropy values to the known population entropy values showed that entropy is a consistent measure of nominal variability. Raw sample entropy is a biased estimator that underestimates the population value. This bias was virtually eliminated through bootstrap resampling from the samples. Bootstrap corrected sample entropy is a sufficient, consistent, minimally biased, population estimator of nominal variability that can be used in further statistical analyses.

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