Independence of an Equivariant and Invariant‎ Functions in Generalized Normal Family‎

In this paper we explain a necessary and sufficent condition for independence between any arbitrary statistics with sufficient statistics which is also maximum likelihood estimator in a general‎ ‎exponential family with location and scale parameter namely generalized normal distribution‎. ‎At the end‎, ‎it is shown that the converse is true except in the asymptotic cases‎.