With the purpose to study as a whole the major part of entropy measures cited in the literature, a mathematical expression is proposed in this paper. In favour of this mathematical tool is the fact that most entropy measures can be obtained as a particular or a limit case of the $H$-entropy functional, and therefore, all those properties which are proved for the functional are also true for its particularizations. Entropy estimates are obtained by replacing probabilities by relative frequencies and their asymptotic distributions are obtained. To finish the asymptotic variance of many entropy statistics are tabulated.
62B10, 94A17, 62E20