Abstract
Abstract Let Xn and X 1 be the largest and smallest order statistics, respectively, of a random sample of size n. Quite generally, Xn and X 1 are approximately independent for n sufficiently large. Minimum n for attaining at least specified levels of independence are developed. Level of independence is measured by the maximum difference between the true values of P(X 1 ≤x 1, Xn ≤xn ) and the corresponding values assuming independence of Xn and X 1. The results apply to all possible distributions for the population sampled. The value of minimum n is the smallest allowable n for the continuous case but can be too large otherwise. Minimum n is finite for all nonzero differences.
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