chapter one is devotod to collect some notion and background informations, which are needed in the next chapters. it also contains some important statements which will be proved in a more general context later in this thesis. in chapter two, we show that if the marginal factor-group is of order np1...pk,n>1, then we obtain a bound for the order of the verbal subgroup. also a bound for the bear-...

‎Basu’s theorem is one of the most elegant results of classical statistics‎. ‎Succinctly put‎, ‎the theorem says‎: ‎if T is a complete sufficient statistic for a family of probability measures‎, ‎and V is an ancillary statistic‎, ‎then T and V are independent‎. ‎A very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statistics‎. ‎In addition ...