Limit Theorems for Bivariate Generalised Order Statistics in Stationary Gaussian Sequences with Random Sample Sizes

摘要

In this paper, we study the limit distribution functions of the (lower-lower), (upper-upper) and (lower-upper) extreme and central-central m -generalised order statistics (m–GOS) of stationary Gaussian sequences under an equi-correlated set up, when the random sample size is assumed to converge weakly and independent of the basic variables. Moreover, sufficient conditions for a weak convergence of generalised quasi-range with random indices are obtained.