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.