  Shannon and Renyi entropies are quantitative measures of uncertainty in a
data set. They are developed by Renyi in the context of entropy theory. These
measures have been studied in the case of the multivariate t-distributions. We
extend these tools to the class of multivariate skew t-distributions and then
to more families of finite mixture of multivariate skew t distributions. In
particular, by using generalized Holder inequality and some properties of
multinomial theorem, we find upper and lower bounds of entropies for these
families. An approximate value of these entropies can be calculated. In
addition, an asymptotic expression for Renyi entropy is given by approximation
and by using some inequalities and properties of Lp spaces. Finally, we give a
real data examples to illustrate the behavior of entropy of the mixture model
under consideration.
