A New Integral Representation of the Coverage Probability of a Random Convex Hull
作者: Won Son Chi Tim Ng Johan Lim
刊名: Communications for Statistical Applications and Methods, 2015, Vol.22 (1)
来源数据库: Communications for Statistical Applications and Methods
DOI: 10.5351/CSAM.2015.22.1.069
关键词: Coverage probabilityintegral representationrandom convex hullrandom pointsstochastic geometry.
原始语种摘要: In this paper, the probability that a given point is covered by a random convex hull generated by independent and identically-distributed random points in a plane is studied. It is shown that such probability can be expressed in terms of an integral that can be approximated numerically by function-evaluations over the grid-points in a 2-dimensional space. The new integral epresentation allows such probability be computed efficiently. The computational burdens under the proposed integral representation and those in the existing literature are compared. The proposed method is illustrated through numerical examples where the random points are drawn from (i) uniform distribution over a square and (ii) bivariate normal distribution over the two-dimensional Euclidean space. The applications of...
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  • points 
  • computational 计算的
  • distributed 分布的
  • bivariate 双变数
  • existing 现行
  • numerically 数字上
  • identically 同一样
  • random 随机的
  • square 正方形
  • integral 积分