Probability distribution and entropy as a measure of uncertainty

TL;DR

This paper explores the relationship between probability distributions and their entropy, defining entropy as a measure of uncertainty through a variational approach without assuming the entropy property.

Contribution

It introduces a variational definition of entropy as a measure of uncertainty, linking probability distributions to their maximizable entropy forms without assuming entropy properties.

Findings

Defines entropy I as a measure of uncertainty via variational relationship

Establishes connection between probability distributions and their maximum entropy forms

Provides a framework for understanding entropy without assuming its properties

Abstract

The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability distribution of a random variable x by a variational relationship, a definition underlying the maximization of entropy for corresponding distribution.