Tag Archives: First Fundamental Form

On the Comparison of Statistical Curvature with Gaussian Curvature (Published)

Efron [1] introduced the new statistical curvature to measure the shape of a one-parameter exponential family.  This family, through the sample space of all possible probability distributions, can be considered a “straight line”. In this paper, using the student t-distribution, we compare this new statistical curvature with the classical Gaussian curvature. Efron’s defined curvature has greatly reduced the quantities of curvature. In order to compare Efron’s statistical curvature with the Gaussian curvature this paper will look at the degree of freedom.

Keywords: Comparison, Covariance Matrix, Curvature Reduction, Degree of Freedom, First Fundamental Form