Exponentiated extended extreme value distribution: Properties, estimation, and applications in applied fields

M. G. M. Ghazal; Yusra A. Tashkandy; Oluwafemi Samson Balogun; M. E. Bakr; M. G. M. Ghazal; Yusra A. Tashkandy; Oluwafemi Samson Balogun; M. E. Bakr

doi:10.3934/math.2024857

AIMS Mathematics

2024, Volume 9, Issue 7: 17634-17656. doi: 10.3934/math.2024857

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Research article Special Issues

Exponentiated extended extreme value distribution: Properties, estimation, and applications in applied fields

1.
Department of Mathematics, Faculty of Science, Minia University, Minia 61519, Egypt
2.
Department of Mathematics, College of Education, University of Technology and Applied Sciences, Al-Rustaq 329, Sultanate of Oman
3.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
4.
Department of Computing, University of Eastern Finland, FI-70211, Finland

Received: 19 February 2024 Revised: 07 May 2024 Accepted: 16 May 2024 Published: 22 May 2024
MSC : 60E05, 62F10, 62H12

The proposed article introduces a novel three-parameter lifetime model called an exponentiated extended extreme-value (EEEV) distribution model. The EEEV distribution is characterized by increasing or bathtub-shaped hazard rates, which can be advantageous in the context of reliability. Various statistical properties of the distribution have been derived. The article discusses four estimation methods, namely, maximum likelihood, least squares, weighted least squares, and Cramér-von Mises, for EEEV distribution parameter estimation. A simulation study was carried out to examine the performance of the new model estimators based on the four estimation methods by using the average bias, mean squared errors, relative absolute biases, and root mean square error. The flexibility and significance of the EEEV distribution are demonstrated by analyzing three real-world datasets from the fields of medicine and engineering. The EEEV distribution exhibits high adaptability and outperforms several well-known statistical models in terms of performance.
- exponentiated extended extreme value distribution,
- mathematical statistics,
- hazard rate,
- estimation methods,
- simulations,
- lifetime data
Citation: M. G. M. Ghazal, Yusra A. Tashkandy, Oluwafemi Samson Balogun, M. E. Bakr. Exponentiated extended extreme value distribution: Properties, estimation, and applications in applied fields[J]. AIMS Mathematics, 2024, 9(7): 17634-17656. doi: 10.3934/math.2024857

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Abstract

The proposed article introduces a novel three-parameter lifetime model called an exponentiated extended extreme-value (EEEV) distribution model. The EEEV distribution is characterized by increasing or bathtub-shaped hazard rates, which can be advantageous in the context of reliability. Various statistical properties of the distribution have been derived. The article discusses four estimation methods, namely, maximum likelihood, least squares, weighted least squares, and Cramér-von Mises, for EEEV distribution parameter estimation. A simulation study was carried out to examine the performance of the new model estimators based on the four estimation methods by using the average bias, mean squared errors, relative absolute biases, and root mean square error. The flexibility and significance of the EEEV distribution are demonstrated by analyzing three real-world datasets from the fields of medicine and engineering. The EEEV distribution exhibits high adaptability and outperforms several well-known statistical models in terms of performance.

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