A simulation study of a new family of test statistics for the Behrens-Fisher problem

Purpose - To provide a new family of test statistics to solve the Behrens-Fisher problem and to compare it with the classic test statistics through a different simulation studies. Design/methodology/approach - A general procedure for testing composite hypothesis to k samples of different size problems on the basis of the Renyi's divergence is used to develop a new parametric family of test statistics that contains as a particular case the classical likelihood ratio test. The scope of the paper is to find out if some member of the new family of test statistics it is preferable to the classical ones. Findings - Some members of the new parametric family of test statistics behave remarkably well in comparison to the classic ones, as the different computational studies reveal. Originality/value - This paper offers a new way to solve the Behrens-Fisher problem that it is preferable in some cases to the known procedures.