Title: Information-geometrical characterization of statistical models which are statistically equivalent to probability simplexes,
Abstract: The probability simplex is the set of all probability distributions on a
finite set and is the most fundamental object in the finite probability theory.
In this paper we give a characterization of statistical models on finite sets
which are statistically equivalent to probability simplexes in terms of
$\alpha$-families including exponential families and mixture families. The
subject has a close relation to some fundamental aspects of information
geometry such as $\alpha$-connections and autoparallelity.