Perceptive Statistical Variability Indicators

TL;DR

This paper introduces perceptive statistical measures to quantify variability and invariability, linking them to entropy concepts and applying them to ocean wind wave data for better understanding of their relationship.

Contribution

It proposes two novel perceptive statistical indicators based on entropy to measure variability and invariability, bridging theoretical concepts with real-world oceanographic data.

Findings

The measures effectively characterize variability and invariability in probability distributions.

Application to ocean wind wave data demonstrates practical relevance.

The approach clarifies the relationship between variability and uncertainty.

Abstract

The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on their differences and then on their common characteristics. Inspired with the definition of average number of equally probable events based on entropy concept in probability theory, the article introduced two related perceptive statistical measures which indicate the same variability as the basic probability distribution. First is the equivalent number of a hypothetical distribution with one sure and all the other impossible outcomes which indicates variability. Second is the appropriate equivalent number of a hypothetical distribution with all equal probabilities which indicates invariability. The article interprets the common properties of variability and uncertainty on theoretical distributions and on ocean-wide wind wave directional properties by using the long term observations compiled in the Global Wave Statistics.