Shape of Traveling Densities with Extremum Statistical Complexity

TL;DR

This paper investigates how the statistical complexity of combined traveling densities varies, identifying the shapes that produce extreme complexity values across different distribution types.

Contribution

It extends previous work by analyzing crossing behaviors of exponential and gamma distributions, revealing the shapes that maximize or minimize complexity.

Findings

Identified density shapes with extremum complexity during crossing.

Extended analysis to exponential and gamma distributions.

Provided insights into the behavior of statistical complexity in dynamic systems.

Abstract

In this paper, we analyze the behavior of statistical complexity in several systems where two identical densities that travel in opposite direction cross each other. Besides the crossing between two Gaussian, rectangular and triangular densities studied in a previous work, we also investigate in detail the crossing between two exponential and two gamma distributions. For all these cases, the shape of the total density presenting an extreme value in complexity is found.