A new alpha power type-II Lomax distribution with applications to radiation and materials sciences

Hazim G. Kalt; Anis Ben Ghorbal; Ibrahim Elbatal; Ahmed Z. Afify; Hisham A. Mahran; Hazim G. Kalt; Anis Ben Ghorbal; Ibrahim Elbatal; Ahmed Z. Afify; Hisham A. Mahran

doi:10.3934/math.2026334

AIMS Mathematics

2026, Volume 11, Issue 3: 8134-8167. doi: 10.3934/math.2026334

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A new alpha power type-II Lomax distribution with applications to radiation and materials sciences

1.
Department of Mathematics, University of Kerbala, Karbala, Iraq
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Statistics, Mathematics, and Insurance, Benha University, Benha 13511, Egypt
4.
Department of Statistics, Mathematics and Insurance, Ain Shams University, Cairo 11566, Egypt

Received: 25 January 2026 Revised: 05 March 2026 Accepted: 17 March 2026 Published: 27 March 2026
MSC : 60E05, 62E10, 62F10, 62N05

This study introduces a novel three-parameter continuous model, termed the alpha power type II Lomax (APIILx) distribution, which is constructed by integrating the alpha power type II-G (APII-G) family with the Lomax distribution. The proposed model demonstrates remarkable flexibility and is capable of capturing a wide variety of distributional shapes. Its key statistical properties are rigorously derived. The model parameters are estimated using eight frequentist estimation methods, and the performance of these estimators is evaluated through extensive Monte Carlo simulations under diverse parameter configurations and sample sizes. The simulation findings confirm the consistency and efficiency of the estimators. To identify the most effective estimation procedure for the APIILx parameters, the estimators are ranked based on both partial and overall ranking criteria. Furthermore, the practical utility of the APIILx distribution is demonstrated through applications to four real-world datasets from medical, biomedical, and engineering sciences. The APIILx model consistently outperforms several well-known competing distributions in modeling radiotherapy, biomedical, and materials science data, highlighting its strong robustness and enhanced adaptability for diverse real-world applications.
- alpha power type II-G family,
- Lomax distribution,
- maximum likelihood estimation,
- simulation study,
- engineering and radiation data
Citation: Hazim G. Kalt, Anis Ben Ghorbal, Ibrahim Elbatal, Ahmed Z. Afify, Hisham A. Mahran. A new alpha power type-II Lomax distribution with applications to radiation and materials sciences[J]. AIMS Mathematics, 2026, 11(3): 8134-8167. doi: 10.3934/math.2026334

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Abstract

This study introduces a novel three-parameter continuous model, termed the alpha power type II Lomax (APIILx) distribution, which is constructed by integrating the alpha power type II-G (APII-G) family with the Lomax distribution. The proposed model demonstrates remarkable flexibility and is capable of capturing a wide variety of distributional shapes. Its key statistical properties are rigorously derived. The model parameters are estimated using eight frequentist estimation methods, and the performance of these estimators is evaluated through extensive Monte Carlo simulations under diverse parameter configurations and sample sizes. The simulation findings confirm the consistency and efficiency of the estimators. To identify the most effective estimation procedure for the APIILx parameters, the estimators are ranked based on both partial and overall ranking criteria. Furthermore, the practical utility of the APIILx distribution is demonstrated through applications to four real-world datasets from medical, biomedical, and engineering sciences. The APIILx model consistently outperforms several well-known competing distributions in modeling radiotherapy, biomedical, and materials science data, highlighting its strong robustness and enhanced adaptability for diverse real-world applications.

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