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