Summary
We prove in this paper a law of Erdös-Rényi type for arrays of independent and identically distributed random variables. The relationships of our theorem with similar results obtained in the theory of runs and spacings are investigated. Applications include the evaluation of the rate of convergence of Erdös-Rényi maxima in limiting cases and a generalization of a Theorem of Erdös and Révész on runs.
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Deheuvels, P. On the Erdös-Rényi theorem for random fields and sequences and its relationships with the theory of runs and spacings. Z. Wahrscheinlichkeitstheorie verw Gebiete 70, 91–115 (1985). https://doi.org/10.1007/BF00532239
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DOI: https://doi.org/10.1007/BF00532239