We show that the minimum value of a sample of feasible points uniformly distributed over a linear constraint set is, for concave functions, asymptotically Weibull distributed with shape parameter equal to the dimension of the feasible region.
Nitin R. Patel, Robert L. Smith, (1983) Technical Note—The Asymptotic Extreme Value Distribution of the Sample Minimum of a Concave Function under Linear Constraints. Operations Research 31(4):789-794.
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