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 γ_1,n, γ_2,n, … , γ_n,n are assumed to be pairwise different.