Statistical exponential families: A digest with flash cards

This document describes concisely the ubiquitous class of exponential family distributions met in statistics. The first part recalls definitions and summarizes main properties and duality with Bregman divergences (all proofs are skipped). The second part lists decompositions and related formula of common exponential family distributions. We recall the Fisher-Rao-Riemannian geometries and the dual affine connection information geometries of statistical manifolds. It is intended to maintain and update this document and catalog by adding new distribution items. See the jMEF library, a Java package for processing mixture of exponential families. Available for download at http://www.lix.polytechnique.fr/~nielsen/MEF/ École Polytechnique (France) and Sony Computer Science Laboratories Inc. (Japan). École Polytechnique (France).