高维正态分布族Fisher度量的曲率
Curvature Properties of Fisher Metrics for High-Dimensional Normal Distribution Families
DOI: 10.12677/pm.2025.155160, PDF,   
作者: 熊明月：重庆理工大学理学院，重庆
关键词: 正态分布；Fisher度量；爱因斯坦空间；Normal Distribution； Fisher Metric； Einstein Space
摘要: 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，并且证明了当协方差矩阵Σ为对角矩阵时，正态分布族的参数空间是爱因斯坦空间，其Ricci曲率与度量张量成严格比例关系。
Abstract: 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 Σ 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.
文章引用：熊明月. 高维正态分布族Fisher度量的曲率[J]. 理论数学, 2025, 15(5): 117-129. https://doi.org/10.12677/pm.2025.155160

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