LIMIT theorems of order statistics in Gaussian sequence

Order statistics play an important role in various fields of statistics and its applications. The order statistics often occur in mathematical statistics applications such as nonparametric industrial applications such as life testing economics applications such as finance insurance and auction and military applications such as radar target detection and missile evaluation. The asymptotic theory of extreme order statistics provides in some cases exact but in most cases approximate probabilistic models for random quantities when the extremes govern the laws of interest (strength of materials foods droughts air pollution failure of equipment). The subject of generalized order statistics (gos) has been introduced by Kamps (1995) as a unification of several models of ascendingly ordered random variables. The second object is to study the limit distributions of extreme intermediate and central m-gos as well as m-dgos of a stationary Gaussian sequence under equi-correlated set up.