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Order Statistics Close to a Minimum

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Abstract

A study is performed of the asymptotic distribution of order statistics \(X_{k}^{(n)}\) when size \(n\) of a sample and rank \(k\) grow indefinitely, but \(k/n\to 0\). A similar problem in terms of quantile functions was studied by Teugels for the order statistic \(X_{n-k+1}^{(n)}\) of rank \(n-k+1\).

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REFERENCES

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, 119991, Moscow, Russia

    V. I. Pagurova

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  1. V. I. Pagurova
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Correspondence to V. I. Pagurova.

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Translated by I. Tselishcheva

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Pagurova, V.I. Order Statistics Close to a Minimum. MoscowUniv.Comput.Math.Cybern. 46, 93–98 (2022). https://doi.org/10.3103/S0278641922020078

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  • DOI: https://doi.org/10.3103/S0278641922020078

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