  In this paper, we present a novel test for determining equality in
distribution of matrix distributions. Our approach is based on the integral
squared difference of the empirical Laplace transforms with respect to the
noncentral Wishart measure. We conduct an extensive power study to assess the
performance of the test and determine the optimal choice of parameters.
Furthermore, we demonstrate the applicability of the test on financial and
non-life insurance data, illustrating its effectiveness in practical scenarios.
