A Dually Flat Geometry of the Manifold of F-Escort Probability Distributions

By : Subrahamanian Moosath, K.S, Harsha, K.V.

Page No: 1-12

Abstract
In this paper, we consider a deformed exponential family called F-exponential family. Then on a F-exponential family, we describe a dually flat structure called the c-geometry and we obtain that this c-geometry is the conformal flattening of the (F, G)-geometry for suitable choices of F and G. The potential functions and the dual coordinates are given for the dually flat structure. The dual coordinates are defined using the F-escort probability distributions. Thus one can say that the manifold of F-escort probability distributions is dually flat by the conformal flattening of the (F, G)-geometry defined on the manifold of usual probability distributions. Further a maximum likelihood estimator is defined using the F-escort probability distribution.