**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.