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A Hyperbolic Secant-Squared Distribution via the Nonlinear Evolution Equation and Its Application

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  • Amira F. Daghistani

    (Department of Mathematics, College of Science and Humanities, Imam Abdulrahman Bin Faisal University, Jubail 35811, Saudi Arabia)

  • Ahmed M. T. Abd El-Bar

    (Department of Mathematics, College of Science, Taibah University, Madinah 42353, Saudi Arabia
    Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt)

  • Ahmed M. Gemeay

    (Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt)

  • Mahmoud A. E. Abdelrahman

    (Department of Mathematics, College of Science, Taibah University, Madinah 42353, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Samia Z. Hassan

    (Department of Mathematics, College of Science and Humanities, Imam Abdulrahman Bin Faisal University, Jubail 35811, Saudi Arabia)

Abstract

In this article, we present a hyperbolic secant-squared distribution via the nonlinear evolution equation. Namely, for this equation, the probability density function of the hyperbolic secant-squared (HSS) distribution has been determined. The density of our model has a variety of shapes, including symmetric, left-skewed, and right-skewed. Eight distinct frequent list estimation methods have been proposed for estimating the parameters of our models. Additionally, these estimation techniques have been used to examine the behavior of the HSS model parameters using data sets that were generated randomly. To demonstrate how the findings may be used to model real data using the HSS distribution, we also use real data. Finally, the proposed justification can be applied to a variety of other complex physical models.

Suggested Citation

  • Amira F. Daghistani & Ahmed M. T. Abd El-Bar & Ahmed M. Gemeay & Mahmoud A. E. Abdelrahman & Samia Z. Hassan, 2023. "A Hyperbolic Secant-Squared Distribution via the Nonlinear Evolution Equation and Its Application," Mathematics, MDPI, vol. 11(20), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4270-:d:1258900
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    References listed on IDEAS

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    4. Yang, Xuehua & Wu, Lijiao & Zhang, Haixiang, 2023. "A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    5. Saralees Nadarajah & Samuel Kotz, 2006. "Beta trigonometric distributions," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 5(3), pages 207-224, December.
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