An Inequality on a Bivariate Student's“t”Distribution
Max Halperin · Journal of the American Statistical Association · 1967
Let (xi, yi), i = 0, 1, 2, …, v, v ≥ 1 be independent samples from bivariate normal distributions with zero means, variances σ2 x , σ y 2, and covariances, σ x σ v ρ i , |ρ i| ≤1. Let xi , i=v + 1, ≤, v+n, yi, i = v+1, …, v+m, be independent samples from N (0, σ x ), N(0, σ y ) respectively and independent of (xi, yi ), i = 0, 1, 2, …, v. Let , and let . We show that