Summary
A sequence {X n} of independent and identically distributed (i.i.d.) random variables is considered. Outstanding values in the sequence are those that strictly exceed values preceding them. Let L n be the index of the n-th outstanding value. Limit theorems are given for the sequences \(\left\{ {X_{L_n } } \right\}\) and {L n} and {δ n} where δ n=Ln−Ln−1. A characterization of the exponential distribution in terms of the sequence \(\left\{ {X_{L_n } } \right\}\) is also given.
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Tata, M.N. On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 12, 9–20 (1969). https://doi.org/10.1007/BF00538520
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DOI: https://doi.org/10.1007/BF00538520