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 Electronic Journal of Probability > Vol. 6 (2001) > Paper 3 open journal systems 


Limit Theorems for the Number of Maxima in Random Samples from Planar Regions

Zhi-Dong Bai, National University of Singapore
Hsien-Kuei Hwang, Academia Sinica
Wen-Qi Liang, Academia Sinica
Tsung-Hsi Tsai, Academia Sinica


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.


Full text: PDF

Pages: 1-41

Published on: January 22, 2001
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Electronic Journal of Probability. ISSN: 1083-6489