On the restricted convergence of generalized extreme order statistics
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Generalized order statistics (gos) introduced by Kamps  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 . 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.
AMS Mathematics Subject Classification60F05 62F15 62E20 62G30
Key words and phrasesWeek convergence generalized order statistics generalized extremes continuation of the convergence
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