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Extropy and Some of Its More Recent Related Measures for Concomitants of K -Record Values in an Extended FGM Family

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  • Mohamed A. Abd Elgawad

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
    Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt)

  • Haroon M. Barakat

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt)

  • Metwally A. Alawady

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt)

  • Doaa A. Abd El-Rahman

    (Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt)

  • Islam A. Husseiny

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt)

  • Atef F. Hashem

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
    Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt)

  • Naif Alotaibi

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

Abstract

This study uses an effective, recently extended Farlie–Gumbel–Morgenstern (EFGM) family to derive the distribution of concomitants of K -record upper values (CKRV). For this CKRV, the negative cumulative residual extropy (NCREX), weighted NCREX (WNCREX), negative cumulative extropy (NCEX), and weighted NCEX (WNCEX) are theoretically and numerically examined. This study presents several beautiful symmetrical and asymmetric relationships that these inaccuracy measurements satisfy. Additionally, empirical estimations are provided for these measures, and their visualizations enable users to verify their accuracy.

Suggested Citation

  • Mohamed A. Abd Elgawad & Haroon M. Barakat & Metwally A. Alawady & Doaa A. Abd El-Rahman & Islam A. Husseiny & Atef F. Hashem & Naif Alotaibi, 2023. "Extropy and Some of Its More Recent Related Measures for Concomitants of K -Record Values in an Extended FGM Family," Mathematics, MDPI, vol. 11(24), pages 1-25, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4934-:d:1298677
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    References listed on IDEAS

    as
    1. Qiu, Guoxin, 2017. "The extropy of order statistics and record values," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 52-60.
    2. Fashandi, M. & Ahmadi, Jafar, 2012. "Characterizations of symmetric distributions based on Rényi entropy," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 798-804.
    3. Poruthiyudian Yageen Thomas & Philip Anne & Thankachan Geetha Veena, 2014. "Characterization of Bivariate Distributions Using Concomitants of Generalized (k) Record Values," Statistica, Department of Statistics, University of Bologna, vol. 74(4), pages 431-446.
    4. Manoj Chacko & M. Shy Mary, 2013. "Concomitants of k-record values arising from Morgenstern family of distributions and their applications in parameter estimation," Statistical Papers, Springer, vol. 54(1), pages 21-46, February.
    5. Qiu, Guoxin & Jia, Kai, 2018. "The residual extropy of order statistics," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 15-22.
    6. Islam A. Husseiny & Metwally A. Alawady & Salem A. Alyami & Mohamed A. Abd Elgawad, 2023. "Measures of Extropy Based on Concomitants of Generalized Order Statistics under a General Framework from Iterated Morgenstern Family," Mathematics, MDPI, vol. 11(6), pages 1-17, March.
    7. I. A. Husseiny & A. H. Syam & Barbara Martinucci, 2022. "The Extropy of Concomitants of Generalized Order Statistics from Huang–Kotz–Morgenstern Bivariate Distribution," Journal of Mathematics, Hindawi, vol. 2022, pages 1-11, August.
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