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2001 Limit Theorems for the Number of Maxima in Random Samples from Planar Regions
Zhi-Dong Bai, Hsien-Kuei Hwang, Wen-Qi Liang, Tsung-Hsi Tsai
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Electron. J. Probab. 6: 1-41 (2001). DOI: 10.1214/EJP.v6-76

Abstract

We prove that the number of maximal points in a random sample taken uniformly and independently from a convex polygon is asymptotically normal in the sense of convergence in distribution. Many new results for other planar regions are also derived. In particular, precise Poisson approximation results are given for the number of maxima in regions bounded above by a nondecreasing curve.

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Zhi-Dong Bai. Hsien-Kuei Hwang. Wen-Qi Liang. Tsung-Hsi Tsai. "Limit Theorems for the Number of Maxima in Random Samples from Planar Regions." Electron. J. Probab. 6 1 - 41, 2001. https://doi.org/10.1214/EJP.v6-76

Information

Accepted: 22 January 2001; Published: 2001
First available in Project Euclid: 19 April 2016

zbMATH: 0986.60007
MathSciNet: MR1816046
Digital Object Identifier: 10.1214/EJP.v6-76

Subjects:
Primary: 60D05
Secondary: 60C05

Keywords: central limit theorems , convex polygons , maximal points , multicriterial optimization , Poisson approximations

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