Abstract
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 meann.
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Haroon Mohoumed Barakat received his BS from Alexa. University, Egypt 1976. His Ph. D. in Math. Statist. Moscow State University, Moscow 1986. Since 1986 he has been at the University of Zagazig. In 1998, he received a Professor from Zagazig Univ. In 1999, he was awarded the Egyptian Encouraging State Prize in Mathematics. In 2001, he was awarded the best paper prize in mathematics. His research interests focus on order statistics.
El-Sayed Mahsoub Nigm received his BS from Zagazig University, Egypt 1983. His Ph. D. in math. statist. Zagazig Univ., Egypt 1990. Since 1983 he has been at the University of Zagazig. In 2001, he received assist. Professor from Zagazig Univ. In 2001, he was awarded the best paper prize in mathematics. His research interests focus, on order statistics.
Magdy El-Sayed El-Adll received his BS from Mansoura University, Egypt 1988. His M.Sc. in math. statist. Mansoura Univ., Egypt 1996. Since 1997, he has been at the University of Helwan. In 1997, he received assist. Lecturer from Helwan Univ. His research interests focus on order statistics.
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Barakat, H.M., Nigm, E.M. & El-Adll, M.E. Continuation theorems of the extremes under power normalization. JAMC 10, 1–15 (2002). https://doi.org/10.1007/BF02936201
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DOI: https://doi.org/10.1007/BF02936201