Asymptotic distribution of the normal sample range
For a spherically symmetric, multivariate normal random sample \(X_ i\), \(i=1,2,\dots,n\), the asymptotic distribution of \(\max_{1\leq i<j\leq n}| X_ j-X_ i|\) as \(n\to\infty\) is considered. The number of \(| X_ j-X_ i|\) exceeding a high level has a Poisson limit distribution.
scientific article; zbMATH DE number 436549