DISTRIBUTION OF THE LARGEST EIGENVALUE OF AN ELLIPTICAL WISHART MATRIX AND ITS SIMULATION

Abstract

This paper provides an alternative proof of the derivation of the distribution of the largest eigenvalue of an elliptical Wishart matrix in contrast to the result of CaroLopera et al. (2016). We show the relation between multivariate and matrix-variate t distributions. From this relation, we can generate random numbers drawn from the matrix-variate t distribution. A Monte Carlo simulation is conducted to evaluate the accuracy for the truncated distribution function of the largest eigenvalue of the elliptical Wishart matrix. Exact computation of the distribution of the smallest eigenvalue is also presented.