::::::::::There is a terrible confusion in the literature about a seeming equivalence of ensembles. Nothing of the sort, not even in the so-called thermodynamic limit. It is impossible to define temperature in the microcanonical ensemble, and any one who tries (and there have been many!) is wrong. Tricks or not, if the entropies are different for different probability distributions, which they are, not one entropy will give all three statistics. And since there are only two distributions (binomial and negative binomial) which tending to a limiting distribution (Poisson) in the high temperature limit, there is no such thing as intermediate, or para-,statistics.