Strong Domain of Attraction of Extreme Generalized Order Statistics |
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Authors: | Frank Marohn |
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Institution: | (1) Mathematisch–Geographische Fakultät, Katholische Universität Eichstätt–Ingolstadt, 85071 Eichstätt, Germany |
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Abstract: | It is a well-known result in extreme value theory that the von Mises conditions imply the strong convergence of extreme order statistics. We extend this result to extreme generalized order statistics. A characterization of strong domains of attraction of joint distributions of a fixed number of extreme generalized order statistics by means of the corresponding result for generalized maxima is given. In particular, we determine the asymptotic joint distribution of (upper and lower) extreme generalized order statistics. Finally, we show that the Hill estimator based on extreme generalized order statistics is asymptotic normal. |
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Keywords: | generalized order statistics generalized extreme value distribution strong domain of attraction von Mises condition Hill estimator |
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