Power of Bivariate Studentized Maximum and Minimum Modulus Tests

Abstract

Let t _i = X _i/s, i = 1, 2 be noncentral Student t-variates with noncentrality parameters δ_i, where x ₁, x ₂ and s are independent. The simultaneous distribution of t ₁ and t ₂ is studied and the power function of the studentized maximum and minimum modulus tests are tabulated for significance level 0.05, degrees of freedom 1, 2, 5, 10, 20, 50, ∞ and δ₁, δ₂ =0(1)5. Asymptotically exact approximations to these power functions are discussed. The marginal power of the maximum modulus test is also tabulated.