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.

翻译：本文提出了一种新颖的检验方法，用于判定矩阵分布是否具有相同的分布。该方法基于经验拉普拉斯变换相对于非中心Wishart测度的积分平方差。我们进行了广泛的功效研究以评估该检验的性能，并确定了参数的最优选择。此外，我们通过在金融与非寿险数据上的应用，证明了该检验在实际场景中的有效性。