TITLE:
The Riemannian Structure of the Three-Parameter Gamma Distribution
AUTHORS:
William W. S. Chen, Samuel Kotz
KEYWORDS:
Mean Curvature; Gamma Distribution; Ricci Curvature; Riemannian Geometry; Scalar Curvature; Sectional Curvature
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.3,
March
22,
2013
ABSTRACT: In this paper, we will utilize the results already known in differential geometry and provide an intuitive understanding of the Gamma Distribution. This approach leads to the definition of new concepts to provide new results of statistical importance. These new results could explain Chen [1-3] experienced difficulty when he attempts to simulate the sampling distribution and power function of Cox’s [4,5] test statistics of separate families of hypotheses. It may also help simplify and clarify some known statistical proofs or results. These results may be of particular interest to mathematical physicists. In general, it has been shown that the parameter space is not of constant curvature. In addition, we calculated some invariant quantities, such as Sectional curvature, Ricci curvature, mean curvature and scalar curvature.