Limit distributions of generalized order statistics under power normalization

Abstract

(Generalized order statistics introduced by Ramps (1995a, b) enable a unified approach to several models of ordered random variables, e.g. order statistics, record values, sequential order statistics. The possible limit distri¬butions of generalized order statistics and their domains of attraction under linear normalization are shown in Nasri Roudsari (1996). In this paper the analogous results for power normalization are derived by establishing a trans¬fer theorem. This technique was already used by Christoph and Falk (1996) for ordinary order statistics.

Keywords:

• volme value theory
• p-max stable distribution
• domain of attraction