Limit distributions for the terms of central order statistics under power normalization

In this paper the limiting distributions for sequences of central terms under power nonrandom normalization are obtained. The classes of the limit types having domain of L- attraction are investigated

Limit theory for bivariate central and bivariate intermediate dual generalized order statistics

Burkschat et al. 2003 have introduced the concept of dual generalized order statistics dgos to unify several models that produce descendingly ordered random variables rv’s like reversed order statistics, lower k-records and lower Pfeifer records. In this paper we derive the limit distribution functions df’s of bivariate central and bivariate intermediate m-dgos. It is revealed that the convergence of the marginals of the m-dgos implies the convergence of the joint df. Moreover, we derive the conditions under which the asymptotic independence between the two marginals occurs.Burkschat et al. 2003 have introduced the concept of dual generalized order statistics dgos to unify several models that produce descendingly ordered random variables rv’s like reversed order statistics, lower k-records and lower Pfeifer records. In this paper we derive the limit distribution functions df’s of bivariate central and bivariate intermediate m-dgos. It is revealed that the convergence of the marginals of the m-dgos implies the convergence of the joint df. Moreover, we derive the conditions under which the asymptotic independence between the two marginals occurs

Generalized Order Statistics with Random Indices in a Stationary Gaussian Sequence

In this paper we study the limit distributions of extreme, intermediate and central m-generalized order statistics (gos), as well as m-dual generalized order statistics (dgos), of a stationary Gaussian sequence (sGs) under equi-correlated set up, when the random sample size is assumed to converge weakly. Moreover, the result of extremes is extended to a wide subclass of gos (as well as dgos) which contains the most important models of ordered random variables (rv’s)