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# The Lambert-G Family: Properties, Inference, and Applications

Jamal N. Al Abbasi1, Ahmed Z. Afify2,*, Badr Alnssyan3,*, Mustafa S. Shama4,5

1 Accounting Department, Ashur University, Baghdad, 10011, Iraq
2 Department of Statistics, Mathematics and Insurance, Benha University, Benha, 13511, Egypt
3 Department of Management Information Systems and Production Management, College of Business and Economics, Qassim University, Buraydah, 51452, Saudi Arabia
4 Department of Basic Sciences, Common First Year (CFY), King Saud University, Riyadh, 11362, Saudi Arabia
5 Department of Mathematics and Statistics, Osim Higher Institute of Administrative Science, Osim, 12961, Egypt

* Corresponding Authors: Ahmed Z. Afify. Email: ; Badr Alnssyan. Email:

(This article belongs to the Special Issue: Frontiers in Parametric Survival Models: Incorporating Trigonometric Baseline Distributions, Machine Learning, and Beyond)

Computer Modeling in Engineering & Sciences 2024, 140(1), 513-536. https://doi.org/10.32604/cmes.2024.046533

## Abstract

This study proposes a new flexible family of distributions called the Lambert-G family. The Lambert family is very flexible and exhibits desirable properties. Its three-parameter special sub-models provide all significant monotonic and non-monotonic failure rates. A special sub-model of the Lambert family called the Lambert-Lomax (LL) distribution is investigated. General expressions for the LL statistical properties are established. Characterizations of the LL distribution are addressed mathematically based on its hazard function. The estimation of the LL parameters is discussed using six estimation methods. The performance of this estimation method is explored through simulation experiments. The usefulness and flexibility of the LL distribution are demonstrated empirically using two real-life data sets. The LL model better fits the exponentiated Lomax, inverse power Lomax, Lomax-Rayleigh, power Lomax, and Lomax distributions.

## Keywords

APA Style
Abbasi, J.N.A., Afify, A.Z., Alnssyan, B., Shama, M.S. (2024). The lambert-g family: properties, inference, and applications. Computer Modeling in Engineering & Sciences, 140(1), 513-536. https://doi.org/10.32604/cmes.2024.046533
Vancouver Style
Abbasi JNA, Afify AZ, Alnssyan B, Shama MS. The lambert-g family: properties, inference, and applications. Comput Model Eng Sci. 2024;140(1):513-536 https://doi.org/10.32604/cmes.2024.046533
IEEE Style
J.N.A. Abbasi, A.Z. Afify, B. Alnssyan, and M.S. Shama "The Lambert-G Family: Properties, Inference, and Applications," Comput. Model. Eng. Sci., vol. 140, no. 1, pp. 513-536. 2024. https://doi.org/10.32604/cmes.2024.046533

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