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SHANTI S. GUPTA and others, On the order statistics from equally correlated normal random variables, Biometrika, Volume 60, Issue 2, August 1973, Pages 403–413, https://doi.org/10.1093/biomet/60.2.403
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Abstract
Let X1, …, XN be N standardized normal variables with correlation matrix {ρij} and let X1 ≤ … ≤ X(N) denote the ordered Xi. Besides some general distribution theory this paper deals with the case where ρij θ ρ(ρ > 0) for all i and j (i ≠ j). Let FN (H; ρ) denote the probability that X(N) ≤ H. Gupta (1963a) discussed the evaluation of the multivariate normal integral and computed the function FN(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 FN(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.