×

The limit distribution of the largest interpoint distance for distributions supported by a \(d\)-dimensional ellipsoid and generalizations. (English) Zbl 1384.60044

Summary: We study the asymptotic behaviour of the maximum interpoint distance of random points in a \(d\)-dimensional ellipsoid with a unique major axis. Instead of investigating only a fixed number of \(n\) points as \(n\) tends to \(\infty\), we consider the much more general setting in which the random points are the supports of appropriately defined Poisson processes. Our main result covers the case of uniformly distributed points.

MSC:

60D05 Geometric probability and stochastic geometry
60F05 Central limit and other weak theorems
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G70 Extreme value theory; extremal stochastic processes
62E20 Asymptotic distribution theory in statistics
PDFBibTeX XMLCite
Full Text: DOI Euclid