An Inequality on a Bivariate Student's“t”Distribution

Abstract

Let ( x i , y i ), i = 0, 1, 2, …, v, v ≥ 1 be independent samples from bivariate normal distributions with zero means, variances σ 2 x , σ y 2 , and covariances, σ x σ v ρ i , |ρ i | ≤1. Let x i , i = v + 1, ≤, v+n, y i , i = v +1, …, v+m , be independent samples from N (0, σ x ), N (0, σ y ) respectively and independent of ( x i , y i ), i = 0, 1, 2, …, v. Let , and let . We show that