Quantile estimates of entropy uncertainty for distributions supported on bounded interval

Medical Cybernetics and Computer Science Department, Medical Institute of Penza State University, 40 Krasnaya Street, Penza, 440026, Russian Federation

^* Corresponding author: polosin-vitalij@yandex.ru

Abstract

Formulas for calculating the Shannon information entropy and the entropy uncertainty interval are obtained, which are based on calculating quantile estimates of random variable distributions and are set over a limited range of random variable values supported both on a semi-infinite interval and on the entire real line. In this paper, using the example of a generalized beta distribution of the first kind, the possibility of determining quantiles for the entire variety of possible shapes of a given distribution subfamily is illustrated. To assess the quality of the approximation construction, a study was conducted, the purpose of which was to compare estimates of the uncertainty of a complex system using analytically specified information entropy for the Kumaraswamy distribution and information entropy obtained on the basis of an approximating formula using quantile estimates of the Kumaraswamy distribution. Based on the study, it is shown that when choosing the sampling intervals specified by the percentiles of the distribution, the approximation error did not exceed 1% for the range of the most used parameters of the power and shape of the Kumaraswamy distribution.