The geometrical structure of the parameter space of the two-dimensional normal distribution |
| |
Authors: | Yoshiharu Sato Kazuaki Sugawa Michiaki Kawaguchi |
| |
Institution: | Division of Information Engineering, Hokkaido University, Sapporo, Japan |
| |
Abstract: | The differential geometrical consideration of the parameter space, especially as a Riemannian geometry, was initiated by C.R. Rao in 1945. This approach appears to be important for the problem of estimation and test of hypotheses as well as for applications to physical problems. It has been shown that the parameter spaces of univariate normal distribution, univariate exponential distribution and multinomial distribution are Riemannian spaces of constant curvature. In the present paper the discussion is confined to the parameter space of the two-dimensional normal distribution. It has been shown that in general the parameter space is not necessarily of a constant curvature and that, if the correlation coefficient vanishes, the parameter space becomes an Einstein space. In addition, some invariant quantities, as sectional curvature, mean curvature and scalar curvature, have been calculated. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|