# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1905.11955