Limit distributions of generalized order statistics in a stationary Gaussian sequence

Abstract

In this paper we study the limit distributions of extreme, intermediate and central m-generalized order statistics, as well as m-dual generalized order statistics, of a stationary Gaussian sequence under equi-correlated set up. Moreover, the result of extremes is extended to a wide subclass of generalized order statistics, as well as dual generalized order statistics, when the parameters y1, n, y2, n,..., yn, n are assumed to be pairwise different.

Mathematics Subject Classification (2010): 60G70, 62G30.

Keywords: Gaussian sequence, generalized order statistics, dual generalized order statistics