Summary
Let X 1, X 2,... denote an i.i.d. sequence of real valued random variables which ly in the domain of attraction of a stable law Q with index 0<α<1. Under a von Mises condition we show that the sum of order statistics
converges to Q with respect to the norm of total variation if for instance min(k(n), r(n))→∞.
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Janssen, A. Uniform convergence of sums of order statistics to stable laws. Probab. Th. Rel. Fields 78, 261–271 (1988). https://doi.org/10.1007/BF00322023
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DOI: https://doi.org/10.1007/BF00322023