On a Geometrical Representation of Probability Distributions and its use in Statistical Inference.

Abstract

ABSTRACT: This paper has been divided into six sections. The first three sections are confined to the consideration of the geometry of a sa.mple space with finite number of points : the first is concerned with the representation of a single probability distribution by a point in a finite dimensional Euclidean space and the geometrical interpretation of the laws of probability theory; the second deals with the relationship between two probability distributions defined on the same space and tbe third gives some results of differential geometry applied to such a space and geometrical representation of Fisher's information matrix. The fourth section indicates bow the concepts can be extended to general probability measures defined on a general measurable space. The fifth section gives an inadequate account of the nse of the concepts developed earlier to problems of statistical inference. The last section is not directly concerned with distance, but contains a numder of allied concepts.