Open AccessTechnical Note—The Asymptotic Extreme Value Distribution of the Sample Minimum of a Concave Function under Linear Constraints
Author(s) -
Nitin R. Patel,
Robert L. Smith
Publication year - 1983
Publication title -
operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.797
H-Index - 140
eISSN - 1526-5463
pISSN - 0030-364X
DOI - 10.1287/opre.31.4.789
Subject(s) - concave function , mathematics , constraint (computer aided design) , weibull distribution , sample (material) , extreme value theory , dimension (graph theory) , function (biology) , value (mathematics) , mathematical optimization , distribution (mathematics) , set (abstract data type) , bellman equation , linear programming , extreme point , mathematical analysis , combinatorics , statistics , computer science , geometry , regular polygon , chemistry , chromatography , evolutionary biology , biology , programming language
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.
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