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Characterizations based on the numbers of near-order statistics

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  • M. Akbari
  • M. Fashandi
  • Jafar Ahmadi

Abstract

In the present work, some characterization results are established based on the number of observations near the order statistics. Under some conditions, it is shown that the parent distribution can be uniquely determined by the moments of the number of observations in a random sample that fall within a left-hand or right-hand neighborhood of a specific order statistic. It is proved that the underlying distribution $$F$$ F belongs to the class of symmetric distributions if and only if the first moment of the number of observations in the right neighborhood of the $$k$$ k th order statistic and in the left neighborhood of the $$(n-k+1)$$ ( n - k + 1 ) th order statistic from a sample of size $$n$$ n are equal. Also, characterizations of the exponential distribution are presented. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • M. Akbari & M. Fashandi & Jafar Ahmadi, 2016. "Characterizations based on the numbers of near-order statistics," Statistical Papers, Springer, vol. 57(1), pages 21-30, March.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:1:p:21-30
    DOI: 10.1007/s00362-014-0636-0
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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. 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.
    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. 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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