# On the maximal halfspace depth of permutation-invariant distributions on the simplex

## TL;DR

This paper calculates the maximum halfspace depth for permutation-invariant distributions on the probability simplex, using stochastic ordering results originally applied to the Behrens-Fisher problem, advancing understanding of distribution depth in high-dimensional probability spaces.

## Contribution

It introduces a method to compute maximal halfspace depth for a specific class of distributions on the simplex, linking stochastic ordering to distribution depth analysis.

## Key findings

- Derived explicit formulas for maximal halfspace depth.
- Connected stochastic ordering results to distribution depth computations.
- Extended the application of stochastic ordering beyond traditional contexts.

## Abstract

We compute the maximal halfspace depth for a class of permutation-invariant distributions on the probability simplex. The derivations are based on stochastic ordering results that so far were only showed to be relevant for the Behrens-Fisher problem.