The most efficient linear combination of the Sign and the Maesono tests for p-normal distributions

In (Burgio and Nikitin, 2001) the linear combination G= aS + bW of the Sign test S and the Wilcoxon test W was studied. The Pitman efficiency of G with respect to Student's t, in the case of location parameters, and its maximum with respect to a and b were calculated and it was obtained that S and W are locally most powerful and Pitman optimal signed rank tests for the Laplace and the logistic densities. In this paper, we obtain the most efficient G combined test when the parent distribution belongs to a certain p-normal family of densities.