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

Amira F. Daghistani (), Ahmed M. T. Abd El-Bar (), Ahmed M. Gemeay, Mahmoud A. E. Abdelrahman and Samia Z. Hassan
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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
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
Samia Z. Hassan: Department of Mathematics, College of Science and Humanities, Imam Abdulrahman Bin Faisal University, Jubail 35811, Saudi Arabia

Mathematics, 2023, vol. 11, issue 20, 1-17

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.

Keywords: nonlinear evolution equation; hyperbolic secant-squared distribution; left-skewed; estimation techniques; real applications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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