In Kamps [7] generalized order statistics (gos) have been introduced as a unifying
theme for several models of ascendingly ordered random variables (rv’s). The main
aim of this paper is to study the limit joint distribution function (df) of any two
statistics in a wide subclass of the gos model known as m-gos. This subclass contains
many important practical models of gos such as ordinary order statistics (oos), order
statistics with non-integer sample size, and sequential order statistics (sos). The
limit df’s of lower-lower extreme, upper-upper extreme, lower-upper extreme, centralcentral
and lower-lower intermediate m-gos are obtained. It is revealed that the
convergence of the marginals m-gos implies the convergence of the joint df. Moreover, the conditions, under which the asymptotic independence between the two marginalsoccurs, are derived. |
