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The distributions of interrecord fillings. (English. Russian original) Zbl 1375.60047
Discrete Math. Appl. 26, No. 4, 213-226 (2016); translation from Diskretn. Mat. 27, No. 3, 56-73 (2015).
Summary: In a sequence of independent positive random variables with the same continuous distribution function a monotonic subsequence of record values is chosen. A corresponding sequence of record times divides the initial sequence into interrecord intervals. Let \(\alpha_i^j\) (\(i\geqslant 1\), \(j = 1, \dots, i\)) be the number of random variables in the interval between \(i\)-th and \((i + 1)\)-th record moments with values between \((j-1)\)-th and \(j\)-th records. Explicit formulas for the joint distributions of the random variables \(\alpha_i^j,\,1\leqslant j\leqslant i\leqslant n\), are derived, limit theorems for the distributions of \(\alpha_i^j\) for \(i\) \(j\) are proved.
MSC:
60E05 Probability distributions: general theory
60F05 Central limit and other weak theorems
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References:
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