Energy Based Equality of Distributions Testing for Compositional Data

TL;DR

This paper introduces {\alpha}-Energy Based Test ({\alpha}-EBT), a new nonparametric method for testing the equality of multivariate compositional data distributions, demonstrating higher power in simulations.

Contribution

The paper proposes {\alpha}-EBT, a novel nonparametric test for compositional data that outperforms existing methods in power without parametric assumptions.

Findings

{\alpha}-EBT shows higher power in simulations.

The test requires no parametric assumptions.

It effectively compares multivariate compositional distributions.

Abstract

Not many tests exist for testing the equality for two or more multivariate distributions with compositional data, perhaps due to their constrained sample space. At the moment, there is only one test suggested that relies upon random projections. We propose a novel test termed {\alpha}-Energy Based Test ({\alpha}-EBT) to compare the multivariate distributions of two (or more) compositional data sets. Similar to the aforementioned test, the new test makes no parametric assumptions about the data and, based on simulation studies it exhibits higher power levels.