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Numbers of near-maxima for the bivariate case

Author

Listed:
  • Bairamov, I.
  • Stepanov, A.

Abstract

Let be independent and identically distributed random vectors with continuous distribution. Let Kn(a,b1,b2) be the number of sample elements that belong to the open rectangle -- numbers of near-maxima in the bivariate case. In the present paper, we discuss asymptotic properties of Kn(a,b1,b2) and Kn([infinity],0,[infinity]).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:3-4:p:196-205
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    References listed on IDEAS

    as
    1. Hashorva, Enkelejd, 2004. "Bivariate maximum insurance claim and related point processes," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 117-128, August.
    2. Balakrishnan, N. & Stepanov, A., 2004. "A note on the paper of Khmaladze et al," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 415-419, July.
    3. Li, Yun, 1999. "A note on the number of records near the maximum," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 153-158, June.
    4. 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.
    5. Hu, Zhishui & Su, Chun, 2003. "Limit theorems for the number and sum of near-maxima for medium tails," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 229-237, July.
    6. 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.
    7. Khmaladze, E. & Nadareishvili, M. & Nikabadze, A., 1997. "Asymptotic behaviour of a number of repeated records," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 49-58, August.
    8. Pakes, Anthony G. & Li, Yun, 1998. "Limit laws for the number of near maxima via the Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 395-401, November.
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    Cited by:

    1. Dembinska, Anna & Iliopoulos, George, 2012. "On the asymptotics of numbers of observations in random regions determined by order statistics," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 151-160, January.
    2. Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    3. 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.
    4. 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.
    5. Stepanov, Alexei, 2014. "On the use of the Borel–Cantelli lemma in Markov chains," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 149-154.
    6. 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.

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