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

   
@article{EJP76,
	author = {Zhi-Dong Bai and Hsien-Kuei Hwang and Wen-Qi Liang and Tsung-Hsi Tsai},
	title = {Limit Theorems for the Number of Maxima in Random Samples from Planar Regions},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {6},
	year = {2001},
	keywords = {Maximal points, multicriterial optimization, central limit theorems, Poisson approximations, convex polygons.},
	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.},
	pages = {no. 3, 1-41},
	issn = {1083-6489},
	doi = {10.1214/EJP.v6-76},    
        url = {http://ejp.ejpecp.org/article/view/76}}