Limit Laws for Extreme Order Statistics From Strong-Mixing Processes

Abstract

This paper considers the possible limit laws for a sequence of normalized extreme order statistics (maximum, second maximum, etc.) from a stationary strong-mixing sequence of random variables. It extends the work of Loynes who treated only the maximum process. The maximum process leads to limit laws that are the same three types that occur when the underlying process is a sequence of independent random variables. The results presented here show that the possible limit laws for the $k$th maximum process $(k > 1)$ from a strong-mixing sequence form a larger class than can occur in the independent case.