A new truncated unit exponentiated Ailamujia distribution with ranked-based inference and engineering applications

Hana S. Jabarah; Ahlam H. Tolba; Ahmed T. Ramadan; Awad I. El-Gohary; Hana S. Jabarah; Ahlam H. Tolba; Ahmed T. Ramadan; Awad I. El-Gohary

doi:10.3934/math.2025914

AIMS Mathematics

2025, Volume 10, Issue 9: 20466-20504. doi: 10.3934/math.2025914

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Research article

A new truncated unit exponentiated Ailamujia distribution with ranked-based inference and engineering applications

1.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt
2.
Department of Mathematics, Faculty of Basic Science, Galala University, Suez 43713, Egypt

Received: 21 April 2025 Revised: 03 August 2025 Accepted: 08 August 2025 Published: 05 September 2025
MSC : 62F15, 62N02

This study introduces a novel and flexible distribution called the truncated exponentiated Ailamujia (TEA) distribution, designed for modeling bounded lifetime data, particularly in engineering applications. The TEA distribution enhances the flexibility of the classic Ailamujia model by incorporating two shape parameters, allowing it to capture a wide range of hazard rate behaviors, including increasing, decreasing, and bathtub shapes. We investigated the mathematical properties of the TEA distribution, including its probability density function, moments, entropy measures, and order statistics. To estimate the model parameters, several classical and modern techniques are developed and compared, including maximum likelihood estimation (MLE), least squares estimation (LSE), weighted LSE, Cramér-von Mises estimation, maximum product spacing estimation, Anderson-Darling and right-tail Anderson-Darling estimation, Percentile estimation, and Bayesian estimation via the Markov chain Monte Carlo (MCMC) method. The effectiveness and flexibility of the proposed model were validated through extensive Monte Carlo simulations and real-life engineering datasets. The results demonstrate that the TEA distribution consistently provides a better fit compared to several well-known competing models. These findings highlight the practical value of the TEA model for engineers and statisticians working with bounded data of reliability type.
- truncated distributions,
- Ailamujia distribution,
- ranked-based estimation,
- Bayesian inference,
- entropy,
- engineering applications
Citation: Hana S. Jabarah, Ahlam H. Tolba, Ahmed T. Ramadan, Awad I. El-Gohary. A new truncated unit exponentiated Ailamujia distribution with ranked-based inference and engineering applications[J]. AIMS Mathematics, 2025, 10(9): 20466-20504. doi: 10.3934/math.2025914

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Abstract

This study introduces a novel and flexible distribution called the truncated exponentiated Ailamujia (TEA) distribution, designed for modeling bounded lifetime data, particularly in engineering applications. The TEA distribution enhances the flexibility of the classic Ailamujia model by incorporating two shape parameters, allowing it to capture a wide range of hazard rate behaviors, including increasing, decreasing, and bathtub shapes. We investigated the mathematical properties of the TEA distribution, including its probability density function, moments, entropy measures, and order statistics. To estimate the model parameters, several classical and modern techniques are developed and compared, including maximum likelihood estimation (MLE), least squares estimation (LSE), weighted LSE, Cramér-von Mises estimation, maximum product spacing estimation, Anderson-Darling and right-tail Anderson-Darling estimation, Percentile estimation, and Bayesian estimation via the Markov chain Monte Carlo (MCMC) method. The effectiveness and flexibility of the proposed model were validated through extensive Monte Carlo simulations and real-life engineering datasets. The results demonstrate that the TEA distribution consistently provides a better fit compared to several well-known competing models. These findings highlight the practical value of the TEA model for engineers and statisticians working with bounded data of reliability type.

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