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.
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