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On the asymptotics of numbers of observations in random regions determined by order statistics

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  • Dembinska, Anna
  • Iliopoulos, George

Abstract

In this paper, we consider random variables counting numbers of observations that fall into regions determined by extreme order statistics and Borel sets. We study multivariate asymptotic behavior of these random variables and express their joint limiting law in terms of independent multinomial and negative multinomial laws. First, we give our results for samples with deterministic size; next we explain how to generalize them to the case of randomly indexed samples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:151-160
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Hashorva, Enkelejd, 2004. "Bivariate maximum insurance claim and related point processes," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 117-128, August.
    5. 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. Augustynowicz, Aneta, 2020. "Asymptotic behavior of proportions of observations falling to random regions determined by central order statistics," Statistics & Probability Letters, Elsevier, vol. 162(C).
    2. Rasbagh Vasudeva & J. Vasantha Kumari, 2014. "Asymptotic behaviour of near-maxima of Gaussian sequences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 861-866, October.
    3. Jasiński, Krzysztof, 2016. "Asymptotic normality of numbers of observations near order statistics from stationary processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 259-263.

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