The exponentiated modified Lindley distribution with diverse biomedical and epidemiological applications

Ammar M. Sarhan; Asamh Saleh M. Al Luhayb; Reid Alotaibi; M. E. Sobh; Ammar M. Sarhan; Asamh Saleh M. Al Luhayb; Reid Alotaibi; M. E. Sobh

doi:10.3934/math.2026093

AIMS Mathematics

2026, Volume 11, Issue 1: 2313-2340. doi: 10.3934/math.2026093

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The exponentiated modified Lindley distribution with diverse biomedical and epidemiological applications

1.
Mathematics Department, Faculty of Science, Mansoura University, Egypt
2.
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada
3.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
4.
Department of Mathematics, College of Science and Humanities, Shaqra University, Shaqra, Saudi Arabia

Received: 26 November 2025 Revised: 07 January 2026 Accepted: 14 January 2026 Published: 26 January 2026
MSC : 62E10, 62N05, 62F10, 62F15

This study presents a new two-parameter lifetime model, the exponentiated modified Lindley distribution, which extends the flexibility of the traditional modified Lindley distribution. The proposed model was constructed using an exponentiation approach that introduces an additional shape parameter, allowing it to accommodate a wide variety of data patterns and hazard rate behaviors. Comprehensive analytical properties were investigated, including moments and reliability characteristics, along with several parameter estimation methods. In addition to classical estimation techniques, a Bayesian estimation procedure was developed for the exponentiated modified Lindley distribution, as well as a bootstrap approach for constructing confidence intervals for the model parameters. A simulation study was conducted to assess the efficiency and robustness of the proposed estimators. Furthermore, applications to real datasets demonstrated that the proposed model provides an improved fit compared to conventional lifetime distributions. These results indicate that the exponentiated modified Lindley distribution is a valuable addition to the class of continuous distributions, offering enhanced adaptability for modeling reliability, survival, and other forms of asymmetric data encountered in applied statistics.
- lifetime modeling,
- parameter estimation,
- computational simulations,
- bootstrap confidence intervals,
- maximum likelihood estimation,
- Bayesian inference
Citation: Ammar M. Sarhan, Asamh Saleh M. Al Luhayb, Reid Alotaibi, M. E. Sobh. The exponentiated modified Lindley distribution with diverse biomedical and epidemiological applications[J]. AIMS Mathematics, 2026, 11(1): 2313-2340. doi: 10.3934/math.2026093

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Abstract

This study presents a new two-parameter lifetime model, the exponentiated modified Lindley distribution, which extends the flexibility of the traditional modified Lindley distribution. The proposed model was constructed using an exponentiation approach that introduces an additional shape parameter, allowing it to accommodate a wide variety of data patterns and hazard rate behaviors. Comprehensive analytical properties were investigated, including moments and reliability characteristics, along with several parameter estimation methods. In addition to classical estimation techniques, a Bayesian estimation procedure was developed for the exponentiated modified Lindley distribution, as well as a bootstrap approach for constructing confidence intervals for the model parameters. A simulation study was conducted to assess the efficiency and robustness of the proposed estimators. Furthermore, applications to real datasets demonstrated that the proposed model provides an improved fit compared to conventional lifetime distributions. These results indicate that the exponentiated modified Lindley distribution is a valuable addition to the class of continuous distributions, offering enhanced adaptability for modeling reliability, survival, and other forms of asymmetric data encountered in applied statistics.

References

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