%0 Journal Article
%T 高维正态分布族Fisher度量的曲率<br>Curvature Properties of Fisher Metrics for High-Dimensional Normal Distribution Families
%A 熊明月
%J Pure Mathematics
%P 117-129
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.155160
%X 本文针对高维情形得到了高维正态分布在Fisher度量下的数量曲率&#65292;并且证明了当协方差矩阵&#931;为对角矩阵时&#65292;正态分布族的参数空间是爱因斯坦空间&#65292;其Ricci曲率与度量张量成严格比例关系。<br>In this paper, the scalar curvature of high-dimensional normal distribution under Fisher metric is obtained for the high-dimensional case, and it is proved that when the covariance matrix &#931; is a diagonal matrix, the parameter space of the normal distribution family is Einstein space, and its Ricci curvature is strictly proportional to the metric tensor.
%K 正态分布&#65292
%K Fisher度量&#65292
%K 爱因斯坦空间<br>Normal Distribution
%K Fisher Metric
%K Einstein Space
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=114885