• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.1-15
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• 2002

In this paper an important stability property of the extremes under power normalizations is discussed. It is proved that the restricted convergence of the Power normalized extremes on an arbitrary nondegenerate interval implies the weak convergence. Moreover, this implication, in an important practical situation, is obtained when the sample size is considered as a random variable distributed geometrically with mean n.