A new family of omega-square-type statistics with Bahadur local optimality for the location family of generalized logistic distributions

We introduce a family of weighted omega-square statistics. show that they provide locally asymptotically optimal goodness-of-fit tests, in the sense Bahadur, for location problem associated with (type iv) generalized logistic distributions. Our paper extends and unifies some results already known classical Cramér–von Mises Anderson–Darling statistics which are respect to hyperbolic secant