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A new statistical distribution via the Phi-4 equation with its wide-ranging applications

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  • Yousef F Alharbi
  • Ahmed M T Abd El-Bar
  • Mahmoud A E Abdelrahman
  • Ahmed M Gemeay

Abstract

This paper presents a new framework based on nonlinear partial differential equations and statistics. For the nonlinear Phi-4 equation, the probability density function of the hyperbolic secant (HS) distribution has been obtained. Our model’s density has various shapes, including left-skewed, symmetric, and right-skewed. Eight distinct estimation approaches have been employed to estimate the parameters of our model. Additionally, the behavior of the HS model parameters was investigated using randomly generated data sets using these estimation techniques. Furthermore, we illustrate the applicability of the HS distribution for modeling real data by applying our results to real data. As a result, it is expected that our proposal will be of significant assistance to the community investigating new distributions based on hyperbolic functions and their applications to real-world data sets.

Suggested Citation

  • Yousef F Alharbi & Ahmed M T Abd El-Bar & Mahmoud A E Abdelrahman & Ahmed M Gemeay, 2024. "A new statistical distribution via the Phi-4 equation with its wide-ranging applications," PLOS ONE, Public Library of Science, vol. 19(11), pages 1-19, November.
    • Handle: RePEc:plo:pone00:0312458
    DOI: 10.1371/journal.pone.0312458
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    References listed on IDEAS

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    1. Ibrahim Alkhairy & M. Nagy & Abdisalam Hassan Muse & Eslam Hussam & Sameh S. Askar, 2021. "The Arctan-X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences," Complexity, Hindawi, vol. 2021, pages 1-14, December.
    2. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.
    3. Virginie Konlack Socgnia & Diane Wilcox, 2014. "A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. Virginie Konlack Socgnia & Diane Wilcox, 2014. "A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-15, June.
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