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

Barakat H. M., Abd Elgawad M. A., Nigm E. M.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 2

267--284

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.

On the restricted convergence of the intermediate and central terms of order statistics

Barakat H. M.

Probability and Mathematical Statistics

2003

Vol. 23, Fasc. 2

229--240

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.