Technical Note—The Asymptotic Extreme Value Distribution of the Sample Minimum of a Concave Function under Linear Constraints

1 August 1983

journal article
Published by Institute for Operations Research and the Management Sciences (INFORMS) in Operations Research

Vol. 31 (4) , 789-794
https://doi.org/10.1287/opre.31.4.789

Abstract

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.

Keywords

FUNCTION
SAMPLE MINIMUM
ASYMPTOTICALLY WEIBULL
ASYMPTOTIC EXTREME
WEIBULL DISTRIBUTED
PARAMETER EQUAL
TECHNICAL NOTE

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