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.
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As the distribution function (d.f.) of the suitably normalized general intermediate (or central) term of order statistics converges on an interval [c, d] to an arbitrary nondecreasing function, the continuation of this (weak) convergence on the whole real line to an intermediate (or central) value distribution is proved.
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