This paper investigates and discusses the use of information divergence, through the widely used Kullback–Leibler (KL) divergence, under the multivariate (generalized) \(\gamma \)-order normal distribution (\(\gamma \)-GND). The behavior of the KL divergence, as far as its symmetricity is concerned, is studied by calculating the divergence of \(\gamma \)-GND over the Student’s multivariate t-distribution and vice versa. Certain special cases are also given and discussed. Furthermore, three symmetrized forms of the KL divergence, i.e., the Jeffreys distance, the geometric-KL as well as the harmonic-KL distances, are computed between two members of the \(\gamma \)-GND family, while the corresponding differences between those information distances are also discussed.

本文通过广泛使用的Kullback-Leibler（KL）散度，在多元（广义）\（\ gamma \）-正态分布（\（\ gamma \）- GND）下，研究并讨论了信息散度的使用。通过计算学生多元t分布上\（\ gamma \）- GND的散度，研究了KL散度的行为（就其对称性而言），反之亦然。还给出并讨论了某些特殊情况。此外，在\（\ gamma \）的两个成员之间计算了KL发散的三种对称形式，即杰弗里斯距离，几何KL以及谐波KL距离。-GND系列，同时还讨论了这些信息距离之间的相应差异。