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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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