Geodesic
On Power Series Related to Multivariate Records
Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 405-416.

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The paper introduces a function defined by a power series in the probabilities of multivariate records in a sequence of independent identically distributed random vectors with continuous components. In the univariate case, this function is always the same, but in the multivariate case there exists a broad variety of such functions determined by distribution copulas. The probabilistic meaning of this function and its derivatives is presented. A calculation method using the Kendall distribution function is given. The concepts of favorableness of copulas for records, record time distribution, and mean record time (without taking into account the order) are introduced. Examples are given.
Keywords: power series, multivariate record, Kendall correlation coefficient.
Mots-clés : copula 
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A. V. Lebedev. On Power Series Related to Multivariate Records. Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 405-416. http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a6/

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

[2] P. Khe, K. A. Borovkov, “Predelnye teoremy dlya indikatorov rekordov v porogovykh $F^\alpha$-skhemakh”, Teoriya veroyatn. i ee primen., 65:3, 521–537 | DOI | MR

[3] C. M. Goldie, S. Resnick, “Records in a partially ordered set”, Ann. Probab., 7:2 (1989), 678–699 | MR

[4] C. M. Goldie, S. Resnick, “Many multivariate records”, Stoch. Proc. and their Appl., 59:2 (1995), 185–216 | DOI | MR

[5] E. Hashorva, J. Hüsler, “Multiple maxima in multivariate samples”, Stat. and Probab. Letters, 75:1 (2005), 11–17 | DOI | MR

[6] A. V. Gnedin, “The chain records”, Electron. J. Probab., 12:26 (2007), 767–786 | MR

[7] I. Bayramoglu, “On the records of multivariate random sequences”, Metrika, 79 (2016), 725–747 | DOI | MR | Zbl

[8] C. Dombry, M. Zott, “Multivariate records and hitting scenarios”, Extremes, 21:2 (2018), 343–361 | DOI | MR

[9] A. V. Lebedev, “Rekordy i vozrastaniya mnogomernykh ekstremumov sluchainykh priznakov chastits v nadkriticheskikh vetvyaschikhsya protsessakh s maksimum-lineinoi nasledstvennostyu”, Teoriya veroyatn. i ee primen., 67:2 (2022), 384–395 | DOI | MR | Zbl

[10] R. B. Nelsen, An Introduction to Copulas, Springer, New York, 2006 | MR

[11] A. J. McNeil, R. Frey, P. Embrechts, Quantitative Risk Management, Princeton University Press, Princeton, NJ, 2005 | MR

[12] P. Barbe, C. Genest, K. Ghoudi, “On Kendall's process”, J. Multivariate Anal., 58:2 (1996), 197–229 | DOI | MR | Zbl

[13] K. Ghoudi, A. Khoudraji, L. Rivest, “Proprietes statistiques des copules de valeurs extremes bidimensionnelles”, Canad. J. Statist., 26:1 (1998), 189–190 | DOI | MR

[14] O. V. Staroverov, Azy matematicheskoi demografii, Nauka, M., 1997