A flexible hyperbolic secant-B family of distributions with applications to lifetime and stress-strength data

Aijaz Ahmad; Ahmed R. El-Saeed; Taha Radwan; Manzoor A. Khanday; Ahlam H. Tolba; Aijaz Ahmad; Ahmed R. El-Saeed; Taha Radwan; Manzoor A. Khanday; Ahlam H. Tolba

doi:10.3934/math.2026691

AIMS Mathematics

2026, Volume 11, Issue 6: 16837-16886. doi: 10.3934/math.2026691

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A flexible hyperbolic secant-B family of distributions with applications to lifetime and stress-strength data

1.
Lincoln University College, Petaling Jaya-47301, Selangor, Malaysia
2.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
4.
Department of Mathematics, Lovely Professional University, Punjab, India
5.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 31 January 2026 Revised: 13 April 2026 Accepted: 13 May 2026 Published: 11 June 2026
MSC : 62A86, 62D05, 62F12, 62F25, 62G07, 62L05, 62L10, 62L12

Despite the availability of continuous distributions, few utilize the modeling potential of trigonometric functions, and none are based on the hyperbolic secant function. To fill this gap, we introduce the hyperbolic Sec-B family of trigonometric distributions. As a specific application, we introduce an adapted half-power logistic distribution (HS-PHLD) that retains a simple two-parameter form while offering greater versatility, particularly in tail behavior and skewness. Our research comprehensively explores this, establishing its fundamental mathematical properties, providing series expansions for its functions, and using both non-Bayesian and Bayesian estimation techniques. Monte Carlo simulations are used to validate the effectiveness of these estimators. Practically speaking, the HS-PHLD outperforms well-established models on three real-world datasets from the engineering and survival domains.
- hyperbolic secant function,
- moments,
- statistical model,
- acturial indicators,
- Bayesian analysis,
- simulation,
- estimations,
- data analysis
Citation: Aijaz Ahmad, Ahmed R. El-Saeed, Taha Radwan, Manzoor A. Khanday, Ahlam H. Tolba. A flexible hyperbolic secant-B family of distributions with applications to lifetime and stress-strength data[J]. AIMS Mathematics, 2026, 11(6): 16837-16886. doi: 10.3934/math.2026691

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Abstract

Despite the availability of continuous distributions, few utilize the modeling potential of trigonometric functions, and none are based on the hyperbolic secant function. To fill this gap, we introduce the hyperbolic Sec-B family of trigonometric distributions. As a specific application, we introduce an adapted half-power logistic distribution (HS-PHLD) that retains a simple two-parameter form while offering greater versatility, particularly in tail behavior and skewness. Our research comprehensively explores this, establishing its fundamental mathematical properties, providing series expansions for its functions, and using both non-Bayesian and Bayesian estimation techniques. Monte Carlo simulations are used to validate the effectiveness of these estimators. Practically speaking, the HS-PHLD outperforms well-established models on three real-world datasets from the engineering and survival domains.

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