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Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings

Author

Listed:
  • Mohamed S. Mohamed

    (Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11341, Egypt)

  • Haroon M. Barakat

    (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 13318, Saudi Arabia)

  • Mohamed A. Abd Elgawad

    (Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
    School of Computer Science and Technology, Wuhan University of Technology, Wuhan 430070, China)

Abstract

The Tsallis entropy is an extension of the Shannon entropy and is used extensively in physics. The cumulative residual Tsallis entropy, which is a generalization of the Tsallis entropy, plays an important role in the measurement uncertainty of random variables and has simple relationships with other important information and reliability measures. In this paper, some novel properties of the cumulative residual Tsallis entropy are disclosed. Moreover, this entropy measure is applied to testing the uniformity, where the limit distribution and an approximation of the distribution of the test statistic are derived. In addition, the property of stability is discussed. Furthermore, the percentage points and power against seven alternative distributions of this test statistic are presented. Finally, to compare the power of the suggested test with that of other tests of uniformity, a simulation study is conducted.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:771-:d:760667
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    References listed on IDEAS

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    1. Mohamed S. Mohamed & Haroon M. Barakat & Salem A. Alyami & Mohamed A. Abd Elgawad & Ahmet Ocak Akdemir, 2021. "Fractional Entropy-Based Test of Uniformity with Power Comparisons," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, July.
    2. Madan Mohan Sati & Nitin Gupta, 2015. "Some Characterization Results on Dynamic Cumulative Residual Tsallis Entropy," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-8, October.
    3. 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.
    4. Mohamed Said Mohamed, 2020. "On Cumulative Tsallis Entropy and Its Dynamic Past Version," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1903-1917, December.
    5. Gu, Rongbao, 2017. "Multiscale Shannon entropy and its application in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 215-224.
    6. Wanke, Peter F., 2008. "The uniform distribution as a first practical approach to new product inventory management," International Journal of Production Economics, Elsevier, vol. 114(2), pages 811-819, August.
    7. G. Rajesh & S. M. Sunoj, 2019. "Some properties of cumulative Tsallis entropy of order $$\alpha $$ α," Statistical Papers, Springer, vol. 60(3), pages 933-943, June.
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    Cited by:

    1. 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.
    2. Surendra Singh & Avdhesh Sharma & Akhil Ranjan Garg & Om Prakash Mahela & Baseem Khan & Ilyes Boulkaibet & Bilel Neji & Ahmed Ali & Julien Brito Ballester, 2023. "Power Quality Detection and Categorization Algorithm Actuated by Multiple Signal Processing Techniques and Rule-Based Decision Tree," Sustainability, MDPI, vol. 15(5), pages 1-30, February.

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