Summary
Let X 1, X 2,..., X n be independent random variables having a common distribution in the domain of normal attraction of a completely asymmetric stable law with characteristic exponent α}(0,1) and support bounded below. Let X n:n ≧X n:n -1≧...≧X n:1 denote the ordered sample. We obtain the rate of convergence of n -1/α (X n:n +...+X n:n-k n+1 ) to the stable limit law as both n and k n »∞. As a consequence we obtain a representation of the sum X n:n +...+X n:n-k n+1 .
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Mijnheer, J. On the rate of convergence of the sum of the sample extremes. Probab. Th. Rel. Fields 79, 317–325 (1988). https://doi.org/10.1007/BF00342230
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DOI: https://doi.org/10.1007/BF00342230