Limit distribution of the maximum of some dependent random variables. (Russian) Zbl 0632.62013

Dzhnejd, M. O.

Teor. Veroyatn. Mat. Stat., Kiev 37, 36-39 (1987).

The author shows for a special sequence of dependent random variables that the maximum of the first n terms, when properly normalized, has the same limiting distribution as if the variables were independent.
The result is a special case of an earlier result of the reviewer [Ann. math. Statistics 43, 516-521 (1972; Zbl 0238.62060); see also the reviewer’s book “The asymptotic theory of extreme order statistics” (1978; Zbl 0381.62039), pp. 176-180, or its Russian edition, Nauka, Moscow (1984), pp. 157-160].

Reviewer: J.Galambos

MSC:

62E20	Asymptotic distribution theory in statistics
62G30	Order statistics; empirical distribution functions

Keywords:

dependent random variables; maximum; limiting distribution

Citations:

Zbl 0238.62060; Zbl 0381.62039