On γ-Decomposition of Probability Distributions

Abstract

The standardization has a function of eliminating such information as expectation and variance from its probability distribution. We shall characterize this function as a decomposition of the distributions into two mutually independent parts, one is expectation and variance, and the other is what this paper deals with. And we will define it, in more general sense than the standardization, as γ-decomposition. It is shown that the sp-curvature of saddlepoint gives the γ-decomposition. The sp-curvature successfully explains the asymptotic normality of distributions. A classical limit theorem, such as the de Moivre and Laplace's, can also be proved in terms of the γ-decomposition with sp-curvature.