Limit theorems for diameter of a random sample in the unit ball

DOI10.1007/s10687-007-0038-yzbMath1164.62003OpenAlexW2077821540MaRDI QIDQ1003304

Michael Mayer, Ilya S. Molchanov

Publication date: 28 February 2009

Published in: Extremes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10687-007-0038-y

zbMATH Keywords

convex hullPoisson processesrandom polytopesinterpoint distance

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Geometric probability and stochastic geometry (60D05) Inference from stochastic processes (62M99) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

Extremal linkage networks ⋮ Limit laws for the diameter of a set of random points from a distribution supported by a smoothly bounded set ⋮ Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution ⋮ Asymptotics of the convex hull of spherically symmetric samples ⋮ Extremal random beta polytopes ⋮ Extreme values for characteristic radii of a Poisson-Voronoi tessellation ⋮ Random convex hulls and extreme value statistics ⋮ Convergence of point processes associated with coupon collector's and Dixie cup problems ⋮ Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to \(U\)-statistics and stochastic geometry ⋮ Smooth tail-index estimation ⋮ Poisson approximation with applications to stochastic geometry ⋮ Asymptotic distribution of the maximum interpoint distance for high-dimensional data ⋮ Asymptotics of Random Resonances Generated by a Point Process of Delta-Interactions

Cites Work

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• Asymptotic distribution of the normal sample range
• Limit theorems for convex hulls
• On the area and perimeter of a random convex hull in a bounded convex set
• On \(\alpha\)-symmetric multivariate characteristic functions
• The limit distribution of the largest interpoint distance from a symmetric Kotz sample
• Central limit theorems for random polytopes
• The distribution of the distance between random points
• Short distances, flat triangles and Poisson limits
• On the Hausdorff distance between a convex set and an interior random convex hull
• Random Geometric Graphs
• Limit Theorems for Certain Functionals of Unions of Random Closed Sets
• Limit laws for the diameter of a random point set
• Rates of convergence for random approximations of convex sets
• Random approximation of convex sets*
• Theory of Random Sets