An Asymptotic Lower Bound for the Entropy of Discrete Populations with Application to the Estimation of Entropy for Uniform Populations

摘要

An asymptotic lower bound for the entropy of a multinomial population with an unknown and perhaps countably infinite number of classes is obtained. This bound is a function of the first k + 1 occupancy numbers of a random sample, and is a useful estimator when most of the sample information is contained in the low order occupancy numbers. (Author)