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Asymptotic behavior of the joint record values, with applications

Author

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  • Barakat, H.M.
  • Abd Elgawad, M.A.

Abstract

The class of limit distribution functions of the joint upper record values, as well as the joint of lower record values, is fully characterized. Sufficient conditions for the weak convergence are obtained. As an application of this result, the sufficient conditions for the weak convergence of the record quasi-range, record quasi-midrange, record extremal quasi-quotient and record extremal quasi-product are obtained. Moreover, the classes of the non-degenerate limit distribution functions of these statistics are derived.

Suggested Citation

  • Barakat, H.M. & Abd Elgawad, M.A., 2017. "Asymptotic behavior of the joint record values, with applications," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 13-21.
    • Handle: RePEc:eee:stapro:v:124:y:2017:i:c:p:13-21
    DOI: 10.1016/j.spl.2016.12.020
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    References listed on IDEAS

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    1. Resnick, Sidney I., 1973. "Limit laws for record values," Stochastic Processes and their Applications, Elsevier, vol. 1(1), pages 67-82, January.
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    Cited by:

    1. Falk, M. & Khorrami Chokami, A. & Padoan, S.A., 2018. "Some results on joint record events," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 11-19.
    2. Wang, Guanjun & Peng, Rui & Xing, Liudong, 2018. "Reliability evaluation of unrepairable k-out-of-n: G systems with phased-mission requirements based on record values," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 191-197.
    3. M. A. Abd Elgawad & H. M. Barakat & Ting Yan, 2020. "Bivariate Limit Theorems for Record Values Based on Random Sample Sizes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 50-67, February.

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