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Bivariate Limit Theorems for Record Values Based on Random Sample Sizes

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Abstract

In this paper, the class of limit distribution functions (df’s) of the joint upper record values with random sample size is fully characterized. Necessary and sufficient conditions, as well as the domains of attraction of the limit df’s are obtained. As an application of this result, the sufficient conditions for the weak convergence of the random of record quasi-ranges, record quasi-midranges, record extremal quasi-quotients and record extremal quasi-products are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.

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Acknowledgments

The authors are grateful to the Editor-in-Chief, Professor Dipak K. Dey, and the referees for suggestions and comments that improved the presentation substantially.

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Authors and Affiliations

  1. School of Computer Science and Technology, Wuhan University of Technology, Wuhan, 430070, China

    M. A. Abd Elgawad

  2. Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt

    M. A. Abd Elgawad

  3. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt

    H. M. Barakat

  4. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Ting Yan

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  1. M. A. Abd Elgawad
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  2. H. M. Barakat
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  3. Ting Yan
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Correspondence to M. A. Abd Elgawad.

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Elgawad, M.A.A., Barakat, H.M. & Yan, T. Bivariate Limit Theorems for Record Values Based on Random Sample Sizes. Sankhya A 82, 50–67 (2020). https://doi.org/10.1007/s13171-019-00167-2

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  • DOI: https://doi.org/10.1007/s13171-019-00167-2

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