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Volume 13
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10.3390/math13203307
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Article

Statistical Analysis of the Induced Ailamujia Lifetime Distribution with Engineering and Bidomedical Applications

by
Mahmoud M. Abdelwahab
1,
Dina A. Ramadan
2,*,
Sunil Kumar
3,
Mustafa M. Hasaballah
4 and
Ahmed Mohamed El Gazar
5
1
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt
3
Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India
4
Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt
5
Department of Basic Sciences, Higher Institute for Commercial Sciences, Almahlla Alkubra 31951, Egypt
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(20), 3307; https://doi.org/10.3390/math13203307
Submission received: 14 September 2025 / Revised: 6 October 2025 / Accepted: 10 October 2025 / Published: 16 October 2025
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Abstract

Accurate modeling of industrial and biomedical data is often challenging due to skewness, heavy tails, and complex variability, which traditional probability distributions fail to capture. To address this, we propose the Induced Ailamujia Lifetime Distribution (IALD), a flexible generalization of the Ailamujia distribution developed via an induced transformation. The IALD accommodates diverse dataset characteristics through a wide range of probability density and hazard rate shapes. Several key statistical properties are derived, including moments, reliability measures, quantile and generating functions, probability weighted moments, and entropy measures. Model parameters are estimated using six classical methods, with their performance assessed through simulation. The practical utility of the IALD is demonstrated using two real datasets from biomedical and industrial fields, where it consistently outperforms existing lifetime models. These results confirm the IALD as a powerful and promising tool for reliability, engineering, and biomedical data analysis.
Keywords: Ailamujia distribution; induced generated family; quantile function; least squares estimation method; real datasets Ailamujia distribution; induced generated family; quantile function; least squares estimation method; real datasets

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MDPI and ACS Style

Abdelwahab, M.M.; Ramadan, D.A.; Kumar, S.; Hasaballah, M.M.; El Gazar, A.M. Statistical Analysis of the Induced Ailamujia Lifetime Distribution with Engineering and Bidomedical Applications. Mathematics 2025, 13, 3307. https://doi.org/10.3390/math13203307

AMA Style

Abdelwahab MM, Ramadan DA, Kumar S, Hasaballah MM, El Gazar AM. Statistical Analysis of the Induced Ailamujia Lifetime Distribution with Engineering and Bidomedical Applications. Mathematics. 2025; 13(20):3307. https://doi.org/10.3390/math13203307

Chicago/Turabian Style

Abdelwahab, Mahmoud M., Dina A. Ramadan, Sunil Kumar, Mustafa M. Hasaballah, and Ahmed Mohamed El Gazar. 2025. "Statistical Analysis of the Induced Ailamujia Lifetime Distribution with Engineering and Bidomedical Applications" Mathematics 13, no. 20: 3307. https://doi.org/10.3390/math13203307

APA Style

Abdelwahab, M. M., Ramadan, D. A., Kumar, S., Hasaballah, M. M., & El Gazar, A. M. (2025). Statistical Analysis of the Induced Ailamujia Lifetime Distribution with Engineering and Bidomedical Applications. Mathematics, 13(20), 3307. https://doi.org/10.3390/math13203307

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