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Measures of Extropy Based on Concomitants of Generalized Order Statistics under a General Framework from Iterated Morgenstern Family

Author

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  • Islam A. Husseiny

    (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)

  • Salem A. Alyami

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

  • 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)

Abstract

In this work, we reveal some distributional characteristics of concomitants of generalized order statistics (GOS) with parameters that are pairwise different, arising from iterated Farlie–Gumbel–Morgenstern (IFGM) family of bivariate distributions. Additionally, the joint distribution and product moments of concomitants of GOS for this family are discussed. Moreover, some well-known information measures, i.e., extropy, cumulative residual extropy (CRJ), and negative cumulative extropy (NCJ), are derived. Applications of these results are given for order statistics, record values, and progressive type-II censored order statistics with uniform marginals distributions. Additionally, the issue of estimating the CRJ and NCJ is looked into, utilizing the empirical technique and the concomitant of GOS. Finally, bivariate real-world data sets have been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1377-:d:1095016
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    References listed on IDEAS

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    1. M. A. Alawady & H. M. Barakat & Shengwu Xiong & M. A. Abd Elgawad, 2022. "Concomitants of generalized order statistics from iterated Farlie–Gumbel–Morgenstern type bivariate distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(16), pages 5488-5504, August.
    2. Narayanaswamy Balakrishnan & Francesco Buono & Maria Longobardi, 2022. "On weighted extropies," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(18), pages 6250-6267, September.
    3. Qiu, Guoxin, 2017. "The extropy of order statistics and record values," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 52-60.
    4. Mohamed S. Mohamed & Alanazi Talal Abdulrahman & Zahra Almaspoor & M. Yusuf & Ning Cai, 2021. "Ordered Variables and Their Concomitants under Extropy via COVID-19 Data Application," Complexity, Hindawi, vol. 2021, pages 1-14, July.
    5. Guoxin Qiu & Kai Jia, 2018. "Extropy estimators with applications in testing uniformity," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 182-196, January.
    6. Haroon M. Barakat & El-Sayed M. Nigm & Islam A. Husseiny, 2021. "Measures of information in order statistics and their concomitants for the single iterated Farlie–Gumbel–Morgenstern bivariate distribution," Mathematical Population Studies, Taylor & Francis Journals, vol. 28(3), pages 154-175, July.
    7. Mohamed S. Mohamed & Haroon M. Barakat & Salem A. Alyami & Mohamed A. Abd Elgawad, 2022. "Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    8. Qiu, Guoxin & Jia, Kai, 2018. "The residual extropy of order statistics," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 15-22.
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    Cited by:

    1. 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.

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