The cumulative entropy has been recently proposed as a measure of information that is alternative to the Shannon differential entropy. In this note, after reviewing its main properties, including various upper and lower bounds, a new result on the cumulative entropies of stochastically ordered random variables is provided. We finally obtain some results on the empirical cumulative entropy, provide an example of estimate of the information content in a lifetime data set, and discuss a case showing the convergence of the standard empirical cumulative entropy to the normal distribution.
More on cumulative entropy
DI CRESCENZO, Antonio;
2010
Abstract
The cumulative entropy has been recently proposed as a measure of information that is alternative to the Shannon differential entropy. In this note, after reviewing its main properties, including various upper and lower bounds, a new result on the cumulative entropies of stochastically ordered random variables is provided. We finally obtain some results on the empirical cumulative entropy, provide an example of estimate of the information content in a lifetime data set, and discuss a case showing the convergence of the standard empirical cumulative entropy to the normal distribution.File in questo prodotto:
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