Optimal Sign Test for One Sample Bivariate Location Model Using an Alternative Bivariate Ranked Set Sample

The aim of this paper is to find optimal alternatives bivariate ranked set sample for one sample location model bivariate sign test. Our numerical and theoretical results indicated that the optimal designs for bivariate sign test are the alternative designs with quantifying order statistics with labels [(r+1)/2, (r+1)/2] when the set size r is odd and {[(r/2)+1, r/2], [r/2, (r/2)+1]} when the set size r is even. The asymptotic distribution and Pitman efficiencies of those designs are derived. Simulation study is conducted to investigate the power of the proposed optimal designs. Illustration us