Performance of Various Entropy Measures: Applications to Pareto and Truncated Pareto Distributions

Abstract

This study considers various entropy measures for Pareto distribution
and Truncated Pareto distribution, and also calculates the loss of
entropy when underlying distribution is truncated Pareto distribution
instead of Pareto distribution. The mathematical expression of entropy
measures was derived for Pareto and Truncated Pareto distribution.
Then the mathematical expression of relative loss was derived to check
the performance of various entropy measures. For Comparison purpose
the study considers a real data set available in the literature and find out
the maximum likelihood estimate for the parameters of Pareto
distribution. The results of the relative loss of entropy measures showed
that the natural phenomenon holds in Shannon, Awad, Renyi and Harvrd
& Charvat entropy measures for Pareto distribution, while in Awad et al.
and Arimoto’s it does not hold. Amongst the four entropy measures the
Shannon entropy measure is considered best because it gives us the
minimum loss of information if one considers Truncated Pareto
distribution instead of Pareto distribution.