The Rate of Convergence in Limit Theorems for Max-Semistable Laws

Abstract

Estimates are obtained of the rate of convergence in limit theorems in the max-scheme of independent identically distributed random variables (i.i.d.r.v.'s) under linear and power normalizations, when the maximum is taken over a subsequence of natural numbers {k(n)} satisfying the condition limn_.,~ k(n + l)/k(n) = r, 1 < r < oo.