- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2021 14 (2)
- Authors
- Khamdamov, Isakjan M.; Chay, Zoya S.
- Contact information
- Khamdamov, Isakjan M.: National University of Uzbekistan named after Mirzo Ulugbek Tashkent, Uzbekistan; ; Chay, Zoya S.: Tashkent University of Information Technologies named after M. al-Khwarizmi Tashkent, Uzbekistan;
- Keywords
- convex hull; convex polygon; Poisson point process; binomial point process; central limit; theorem
- Abstract
A convex hull generated by a sample uniformly distributed on the plane is considered in the case when the support of a distribution is a convex polygon. A central limit theorem is proved for the joint distribution of the number of vertices and the area of a convex hull using the Poisson approximation of binomial point processes near the boundary of the support of distribution. Here we apply the results on the joint distribution of the number of vertices and the area of convex hulls generated by the Poisson distribution given in [6]. From the result obtained in the present paper, in particular, follow the results given in [3, 7], when the support is a convex polygon and the convex hull is generated by a homogeneous Poisson point process
- Pages
- 230–241
- DOI
- 10.17516/1997-1397-2021-14-2-232-243
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/137971
Journal of Siberian Federal University. Mathematics & Physics / Joint Distribution of the Number of Vertices and the Area of Convex Hulls Generated by a Uniform Distribution in a Convex Polygon
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