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

This paper deals with the Pitman most efficient Gr linear combination of the Sign and the Maesono tests for parent distributions belonging to the p-normal family of densities. The most efficient linear combinations G2 and G4 are obtained. It is also shown that G2 (for leptokurtic p-normal distributions) and G4 (for platikurtic p-normal distributions) are much more efficient than Student’s t, with a maximum loss of efficiency of about 3,1% in the near proximity of the normal distribution (p=2).