Geodesic
On the Limit Distributions of Order Statistics
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 159-164

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The limit distribution of the $k$-th order statistic in a sample of size $n$ is considered when $k$ increases as $n^\alpha$, $0\alpha1$, namely when the condition (7) on $k$ is satisfied. The possible types of limit distributions and their domains of attraction are derived. 
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     author = {D. M. \v{C}ibisov},
     title = {On the {Limit} {Distributions} of {Order} {Statistics}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {1964},
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D. M. Čibisov. On the Limit Distributions of Order Statistics. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 159-164. http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a20/