# MaxSkew and MultiSkew: Two R Packages for Detecting, Measuring and Removing Multivariate Skewness

## TL;DR

This paper introduces two R packages, MaxSkew and MultiSkew, designed to detect, measure, test, and reduce multivariate skewness, aiding in data analysis and improving statistical method performance.

## Contribution

The paper presents novel R packages that provide comprehensive tools for analyzing and correcting multivariate skewness in data sets.

## Key findings

- Effective measurement of skewness using multivariate cumulants
- Successful removal of skewness through linear projections
- Application demonstrated on Iris dataset

## Abstract

Skewness plays a relevant role in several multivariate statistical techniques. Sometimes it is used to recover data features, as in cluster analysis. In other circumstances, skewness impairs the performances of statistical methods, as in the Hotelling's one-sample test. In both cases, there is the need to check the symmetry of the underlying distribution, either by visual inspection or by formal testing. The R packages MaxSkew and MultiSkew address these issues by measuring, testing and removing skewness from multivariate data. Skewness is assessed by the third multivariate cumulant and its functions. The hypothesis of symmetry is tested either nonparametrically, with the bootstrap, or parametrically, under the normality assumption. Skewness is removed or at least alleviated by projecting the data onto appropriate linear subspaces. Usages of MaxSkew and MultiSkew are illustrated with the Iris dataset.