New Bounds for the Extreme Values of a Finite Sample of Real Numbers

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• 作者：Crouzeix ; Jean-Pierre ; Seeger ; Alberto
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：1996
• 出版时间：January, 1996
• 年：1996
• 卷：197
• 期：2
• 页码：411-426
• 全文大小：189 K

文摘

We derive new bounds for the smallest valuex_minand the largest valuex_maxof a finite samplex₁,…,x_nof real numbers. Our bounds are obtained by solving two optimization problems, one of them being convex and the other nonconvex. We show that the pair (x_min,x_max) lies in a region bounded by an ellipse and an hyperbola. The corresponding cartesian equations are given in terms of the average and the standard deviation of the sample.