J-measure of uncertainty (JMU) for specified probability distribution

TL;DR

This paper introduces a new J-measure of uncertainty (JMU) based on Jaynes entropy maximization for specific probability distributions, providing explicit formulas, examples, and applications to multidimensional cases.

Contribution

It develops explicit formulas for JMU, demonstrates its calculation for various distributions, and explores its application to multidimensional data and the impact of additional measurements.

Findings

JMU maximizes uncertainty for given distributions

Explicit formulas for JMU are derived and demonstrated

Application to multidimensional variables shows effectiveness

Abstract

In this paper it is shown that in the case of the given probability distribution or histogram using the Jaynes entropy maximum principle an J- measure of uncertainty (JMU) provides the maximum for a given distribution can be constructed. Formulas for the introduced JMU were obtained explicitly and calculations of this new measure for a number of distributions are shown as examples. It is shown using as the example a two-dimensional random variable, the application of the proposed method to the JMU estimation for the multidimensional case. It was made a comparison of the information contained in the histogram of a random variable with the information in the probability distribution obtained as a fitting of this histogram. Moreover studied the influence of an additional measurement of a certain physical quantity on the amount of information.