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Numbers of near bivariate record-concomitant observations

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  • Bairamov, I.
  • Stepanov, A.

Abstract

Let be independent and identically distributed random vectors with continuous distribution. Let L(n) and X(n) denote the nth record time and the nth record value obtained from the sequence of Xs. Let Y(n) denote the concomitant of the nth record value, which relates to the sequence of Ys. We call a near bivariate nth record-concomitant observation if belongs to the open rectangle (X(n)-a,X(n))×(Y(n)-b1,Y(n)+b2), where a,b1,b2>0 and L(n)

Suggested Citation

  • Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:5:p:908-917
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    References listed on IDEAS

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    1. A. Stepanov, 2007. "The number of records within a random interval of the current record value," Statistical Papers, Springer, vol. 48(1), pages 63-79, January.
    2. Bairamov, I. & Stepanov, A., 2010. "Numbers of near-maxima for the bivariate case," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 196-205, February.
    3. Li, Y. & Pakes, Anthony G., 2001. "On the number of near-maximum insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 309-323, June.
    4. Hashorva, Enkelejd & Hüsler, Jürg, 2001. "On the number of points near the multivariate maxima," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 113-124, November.
    5. Hashorva, Enkelejd, 2004. "Bivariate maximum insurance claim and related point processes," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 117-128, August.
    6. Hashorva, Enkelejd, 2003. "On the number of near-maximum insurance claim under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 37-49, February.
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    Cited by:

    1. Alexandre Berred & Alexei Stepanov, 2015. "Asymptotic properties of the number of near minimum-concomitant observations in the case of progressive type-II censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 283-294, April.
    2. N. Balakrishnan & Alexei Stepanov, 2015. "Limit results for concomitants of order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 385-397, May.
    3. Dembińska, Anna & Akbari, Masoumeh & Ahmadi, Jafar, 2021. "On numbers of observations in random regions determined by records for tail-less populations," Statistics & Probability Letters, Elsevier, vol. 179(C).
    4. Raúl Gouet & F. López & Gerardo Sanz, 2015. "On the point process of near-record values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 302-321, June.
    5. Bairamov, Ismihan & Khaledi, Baha-Eldin & Shaked, Moshe, 2014. "Stochastic comparisons of order statistics and their concomitants," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 105-115.
    6. Miguel Lafuente & Raúl Gouet & F. Javier López & Gerardo Sanz, 2022. "Near-Record Values in Discrete Random Sequences," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    7. N. Balakrishnan & A. Stepanov & V. B. Nevzorov, 2020. "North-east bivariate records," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 961-976, November.
    8. Pakhteev, A. & Stepanov, A., 2016. "Simulation of Gamma records," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 204-212.
    9. Stepanov, Alexei, 2014. "On the use of the Borel–Cantelli lemma in Markov chains," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 149-154.
    10. Stepanov, Alexei & Berred, Alexandre & Nevzorov, Valery B., 2016. "Concomitants of records: Limit results, generation techniques, correlation," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 184-188.
    11. Pakhteev, A. & Stepanov, A., 2019. "Discrete records: Limit theorems for their spacings and generation methods," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 134-142.
    12. Bayramoglu, Ismihan & Stepanov, Alexei, 2024. "Asymptotic properties of mth spacings based on records," Statistics & Probability Letters, Elsevier, vol. 208(C).

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