  In this paper we provide the asymptotic theory of the general of
$\phi$-divergences measures, which include the most common divergence measures
: Renyi and Tsallis families and the Kullback-Leibler measure. We are
interested in divergence measures in the discrete case. One sided and two-sided
statistical tests are derived as well as symmetrized estimators. Almost sure
rates of convergence and asymptotic normality theorem are obtained in the
general case, and next particularized for the Renyi and Tsallis families and
for the Kullback-Leibler measure as well. Our theorical results are validated
by simulations.
