Geodesic
The distributions of interrecord fillings
Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 56-73.

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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 $\alpha_i^j \ (i\geqslant 1, \,j = 1, \ldots , i)$ 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 $i-j\to\infty$ are proved.
Keywords: independent random variables, records, record moments, explicit formulas for distributions, limit theorems. 
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O. P. Orlov; N. Yu. Pasynkov. The distributions of interrecord fillings. Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 56-73. http://geodesic.mathdoc.fr/item/DM_2015_27_3_a4/

[1] Nevzorov V.B., Rekordy. Matematicheskaya teoriya, Fazis, Moskva, 2000 | MR

[2] Galambosh Ya., Asimptoticheskaya teoriya ekstremalnykh poryadkovykh statistik, Nauka, M., 1984, 304 pp. | MR

[3] Tata M.N., “On outstanding values in a sequence of random variables”, Z.Wahrscheinlichkeitheor. verw. Geb., 12:1 (1969), 9–20 | DOI | MR | Zbl

[4] Neuts M.F., “Waiting times between record observations”, J. Appl. Probab., 4:1 (1967), 206–208 | DOI | MR | Zbl

[5] Shiryaev A.N., Veroyatnost-1, Izdatelstvo MTsNMO, Moskva, 2007, 81 pp.

[6] Borovkov A.A., Matematicheskaya statistika, Izdatelstvo “Lan”, SPb., 2010, 36 pp.

[7] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v 2-kh tomakh, v. 1, “Mir”, Moskva, 1984, 528 pp. | MR

[8] Pasynkov N.Yu., Raspredeleniya v rekordnykh modelyakh, Diplomnaya rabota, mekh-mat MGU, kafedra teorii veroyatnostei, 2014

[9] Orlov O.P., Predelnye teoremy dlya poryadkovykh raspredelenii v mezhrekordnykh momentakh, Diplomnaya rabota, mekh-mat MGU, kafedra teorii veroyatnostei, 2014