三参数burr分布的几何结构

Geometric structures of the three-parameter burr distribution manifold

摘要

摘要:从信息几何的理论出发,建立了三参数burr分布流形,并得出了三参数burr分布流形的Fisher信息矩阵、逆矩阵、张量、α-联络和黎曼曲率一系列几何性质,同时还给出了三参数burr分布流形的两个子流形并计算了相关的几何性质.利用计算结果和相关结论,可以进一步了解三参数burr分布的几何结构.

Abstract:Based on the theory of information geometry, the three-parameter burr distribution manifold is established, and a series of geometric properties of Fisher information matrix, inverse matrix, tensor, α-connection and Riemannian curvature are calculated.At the same time, we also give two submanifolds of three-parameter burr distribution manifoldsand calculate the related geometric properties. The geometric structure of three-parameter burr distribution can be further understood to solve related problems by using the calculation and relevant conclusions.