  Exponential families comprise a broad class of statistical models and
parametric families like normal distributions, binomial distributions, gamma
distributions or exponential distributions. Thereby the formal representation
of its probability distributions induces a confined intrinsic structure, which
appears to be that of a dually flat statistical manifold. Conversely it can be
shown, that any dually flat statistical manifold, which is given by a regular
Bregman divergence uniquely induced a regular exponential family, such that
exponential families may - with some restrictions - be regarded as a universal
representation of dually flat statistical manifolds. This article reviews the
pioneering work of Shun'ichi Amari about the intrinsic structure of exponential
families in terms of structural stratistics.
