**Instructions and examples for the implementation of approximations for the likelihood ratio statistic for testing the equality of several covariance matrices**

**Instructions for the use of the of the codes of the near-exact distributions for the****likelihood ratio test statistic used to test the sphericity structure of a covariance****matrix.**

**Instructions for the use of the of the codes of the near-exact distributions for the****product of independent Generalized Gamma random variables**

The computational implementation of the near-exact distributions for the product of independent Generalized Gamma random variables was made using the software Mathematica.

This package allows the use of the methodology proposed in the paper: Marques, F.J., Diogo, J., Norouzirad, M., and Bispo, R. (2023). Testing the independence of variables for specific covariance structures: A simulation study, Math. Meth. Appl. Sci., 46 (9) 10421-10434. https://doi.org/10.1002/mma.9130