A dually flat structure on the space of escort distributions

This note studies geometrical structure of the manifold of escort probability distributions and proves that the resultant geometry is dually flat in the sense of information geometry. We use a conformal transformation that flattens the alpha-geometry of the space of the discrete probability distributions in order to realize escort probabilities in the framework of affine differential geometry. Dual pairs of potential functions and affine coordinate systems on the manifold are derived, and the associated canonical divergence is shown to be conformal to the alpha-divergence.