Abstract

Let X = (X1, X2, X3) be a non-singular tri-variate normal vector with zero means. Let T = min{X1, X2, X3}, and I = i iff T = Xi, i = 1, 2, 3. The problem of the identified minimum (I, T) is then to find if its joint distribution determines uniquely X. This problem is solved here in the affirmative. To the best of our knowledge, it was first solved in the bivariate normal case (and partially in the tri-variate normal case) in 1978 in [1].

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