ON THE RESTRICTED CONVERGENCE OF GENERALIZED EXTREME ORDER STATISTICS

Generalized order statistics (gos) introduced by Kamps [8] as a unified approach to several models of order random variables (rv's), e.g., (ordinary) order statistics (oos), records, sequential order statistics (sos). In a wide subclass of gos, included oos and sos, the possible limit distribution functions (df's) of the maximum gos are obtained in Nasri-Roudsari [10]. In this paper, for this subclass, as the df of the suitably normalized extreme gos converges on an interval [c, d] to one of possible limit df's of the extreme gos, the continuation of this (weak) convergence on the whole real line to this limit df is proved.