Extreme value limit laws in the nonidentically distributed case
Let \(X_ 1,X_ 2,..\). be independent, not necessarily identically distributed random variables with distribution functions \(F_ 1,F_ 2,... \), and for each integer \(n\geq 1\) let \(X_{1,n}\leq...\leq X_{n,n}\) denote the order statistics based on \(X_ 1,...,X_ n.\) The asymptotic distributional behavior of the intermediate order statistics \(X_{k,n}\), where \(k=k(n)\), k/n\(\to 1\) and n-k\(\to \infty\), is studied. Under appropriate assumptions on the normalizing and centering constants \(a_ n>0\) and \(b_ n\) and the sequences k(n) and \(F_ n\) a characterization of the class of all possible limiting distributions of \((X_{k,n}-b_ n)/a_ n\) is obtained.
independent, non-identically distributed random variables
characterization of the class of all possible limiting distributions
scientific article; zbMATH DE number 4013751