Using the square-root map p→√ pa probability density function p can be represented as a
point of the unit sphere in the Hilbert space of square-integrable functions. If the density …

Abstract Information geometry provides a geometric approach to families of statistical
models. The key geometric structures are the Fisher quadratic form and the Amari–Chentsov …

The Chernoff information between two probability measures is a statistical divergence
measuring their deviation defined as their maximally skewed Bhattacharyya distance …

An information-geometrical foundation is established for the deformed exponential families
of probability distributions. Two different types of geometrical structures, an invariant …

We construct an infinite-dimensional Hilbert manifold of probability measures on an abstract
measurable space. The manifold, M, retains the first-and second-order features of finite …

In this chapter, we study Information Geometry from a particular non-parametric or functional
point of view. The basic model is a probabilities subset usually specified by regularity …

This article focuses on an important piece of work of the world renowned Indian statistician,
Calyampudi Radhakrishna Rao. In 1945, CR Rao (25 years old then) published a …

The differential-geometric structure of the set of positive densities on a given measure space
has raised the interest of many mathematicians after the discovery by CR Rao of the …

Abstract Information geometry has emerged from the study of the invariant structure in
families of probability distributions. This invariance uniquely determines a second-order …

We generalize the exponential family of probability distributions. In our approach, the
exponential function is replaced by a φ-function, resulting in a φ-family of probability …