The limit distribution of the largest interpoint distance for distributions supported by an ellipse and generalizations

2015/05/07 by Michael Schrempp, Schrempp, Michael
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1505.01597

arxiv created 2015/05/07 · openalex publication_date 2015/05/07 · arxiv updated 2015/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of the maximum interpoint distance of random points in a planar bounded set with an unique major axis and a boundary behaving like an ellipse at the endpoints. Our main result covers the case of uniformly distributed points in an ellipse.

Related

• Limit laws for the diameter of a set of random points from a distribution supported by a smoothly bounded set
• A limit theorem for the maximal interpoint distance of a random sample in the unit ball
• Maximum interpoint distance of high-dimensional random vectors
• Limit Law for the Maximum Interpoint Distance of High Dimensional Dependent Variables
• Euclidean and chemical distances in ellipses percolation