On the order statistics from equally correlated normal random variables
Abstract
Abstract SUMMARY Let X 1 , …, X N be N standardized normal variables with correlation matrix {ρ ij } and let X 1 ≤ … ≤ X ( N ) denote the ordered X i . Besides some general distribution theory this paper deals with the case where ρ ij θ ρ(ρ > 0) for all i and j ( i ≠ j ). Let F N ( H ; ρ) denote the probability that X ( N ) ≤ H . Gupta (1963 a ) discussed the evaluation of the multivariate normal integral and computed the function F N ( H ; ρ) for selected values of N , ρ and H . In the present paper, tables are provided for the percentage points of X ( N ), namely, the values of H satisfying F N ( H ; ρ) = 1θα, when α θ 0010, 0.025, 0.050, 0.100, 0.250; N θ 1(1)10(2)50 and ρ θ 0.100, 0.125, 0.200, 1/3;, 0.375, 0.400,1/2;, 0.600, 0.625, 2/3;, 0.700, 0.750, 0.800, 0.875, 0.900. The method of evaluation of the percentage points is discussed. Specific applications illustrating the use of the tables are given. These applications relate to multiple decision rules, multiple comparison problems and some tests of hypotheses.