On the entropy flows to disorder

TL;DR

This paper investigates the properties of Shannon entropy and its flow curves across gamma, Weibull, and exponential distributions, enhancing understanding of their information-theoretic behavior in statistical processes.

Contribution

It provides a detailed analysis of entropy flows for gamma, Weibull, and exponential distributions, extending the theoretical understanding of their informational properties.

Findings

Derived entropy flow curves for gamma and Weibull distributions

Identified relationships between distribution parameters and entropy flows

Enhanced understanding of entropy behavior in statistical process models

Abstract

Gamma distributions, which contain the exponential as a special case, have a distinguished place in the representation of near-Poisson randomness for statistical processes; typically, they represent distributions of spacings between events or voids among objects. Here we look at the properties of the Shannon entropy function and calculate its corresponding flow curves. We consider univariate and bivariate gamma, as well as Weibull distributions which also include exponential distributions.