Asymptotics in order statistics
Jjam Jan Brands · TU/e Research Portal · 1996
Let F be a probability distribution on lR or on [0,00), sufficiently smooth and with the further properties that F(t) < 1 for all t E lR, and that the first two moments E(X) and E(X 2 ) exist.Let (X n ) be a sequence of independent and identically distributed random variables with distribution F. Let Zn := max{X ll ... ,X n } (n E IN).Then Zn has the (cumulative) distribution P(Zn ~t) = pn(t).The asymptotic behaviour for n -+ 00 of E(Zn) and E(Z~) is studied.!Moreover, for the well-known distributions the existence of complete asymptotic expansions is proven.lThe problem was posed by