Summary
If {X n }, n≧1} is an i.i.d. sequence of continuously distributed random variables, and if n k is for k = l, 2, ... the index of the k-th upper outstanding value of the sequence, the record times sequence is defined as {n k , k≧1, whereas the inter-record times sequence is defined as {Δ k =n k − n k−1, k≧1}. We give here for θ k=n k or Δ k a complete characterization of the sequences {α k } and {β k }} such that P(θ k≦βki.o.) or P(θk≧αki.o.) = 0 or 1.
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Deheuvels, P. The complete characterization of the upper and lower class of the record and inter-record times of an I.I.D. sequence. Z. Wahrscheinlichkeitstheorie verw Gebiete 62, 1–6 (1983). https://doi.org/10.1007/BF00532158
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DOI: https://doi.org/10.1007/BF00532158