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On the asymptotic distribution of the area outside a random convex hull in a disk /

The asymptotic distribution of the area $V_n$ outside the convex hull of $n$ i.i.d. points uniformly distributed on the two-dimensional unit disk is studied. The asymptotic variance of $V_n$ is found to be of the order $n^{-5/3}$ and the asymptotic distribution of $V_n$ is shown to be normal. The re...

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Bibliographic Details
Main Author: Hsing, Tailen, 1955- (Author)
Corporate Authors: United States. Office of Naval Research (sponsoring body.), National Science Foundation (U.S.) (sponsoring body.)
Format: Book
Language:English
Published: College Station, Texas : Department of Statistics, Texas A & M University, 1992.
Series:Technical report (Texas A & M University. Department of Statistics) ; no. 183.
Subjects:
Stochastic geometry.
Integral geometry.
Central limit theorem.
Limit theorems (Probability theory)
Asymptotic distribution (Probability theory)
Dependence (Statistics)
Convex sets.
Point processes.
Mathematical statistics.
Probability theory and stochastic processes > Limit theorems > Central limit and other weak theorems.
Probability theory and stochastic processes > Geometric probability and stochastic geometry > Geometric probability and stochastic geometry.
Description
Summary:The asymptotic distribution of the area $V_n$ outside the convex hull of $n$ i.i.d. points uniformly distributed on the two-dimensional unit disk is studied. The asymptotic variance of $V_n$ is found to be of the order $n^{-5/3}$ and the asymptotic distribution of $V_n$ is shown to be normal. The results are obtained by carefully analyzing the strength of dependence between sample points at different locations close to the boundary of the unit disk.
Item Description:Funding information taken from leaf i.
Physical Description:14 leaves ; 28 cm
Bibliography:Includes bibliographical references (leaf 14).