Uncertainties for symmetric and asymmetric distribution models

Medical Cybernetics and Computer Science Department, Penza State University, 40, Krasnay Str., Penza, 440026, Russia

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

Published online: 17 February 2025

Abstract

The model of the symmetric distribution shows the relationship between both the intervals of entropy uncertainty and the peculiarities of the formation of intervals of parametric uncertainty for symmetric and nonsymmetric distributions. In particular, the proportionality of the entropies of symmetric and non-symmetric distributions is shown. The peculiarity of the formation of entropy features of symmetric and asymmetric distribution is shown. The entropy coefficient of asymmetric distributions is proposed as an independent entropy feature of the shape of asymmetric distributions. The peculiarity of applying the entropy coefficient of a symmetric distribution to the description of the properties of an asymmetric distribution is discussed. In this paper the peculiarity of applying the entropy coefficient of a symmetric distribution to the description of the properties of an asymmetric distribution also is discussed. In particular, it is shown that the use of the entropy feature of a symmetric distribution can be considered as a replacement for an asymmetric distribution near the estimates of the center of random variables by means of its symmetric model intervals of parametric and entropy uncertainty. Such a replacement is possible if the intervals of the models are equal.