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Symmetry
Volume 17
Issue 12
10.3390/sym17122140
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Advances in Discrete Lifetime Modeling: A Novel Discrete Weibull Mixture Distribution with Applications to Medical and Reliability Studies

by
Doha R. Salem
1,
Mai A. Hegazy
1,
Hebatalla H. Mohammad
2,
Zakiah I. Kalantan
3,
Gannat R. AL-Dayian
4,
Abeer A. EL-Helbawy
4,5,* and
Mervat K. Abd Elaal
4,6
1
Department of Statistics, Faculty of Commerce, Al-Azhar University (Girls’ Branch), Tafahna Al-Ashraf 35612, Egypt
2
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3
Department of Statistics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4
Department of Statistics, Faculty of Commerce, Al-Azhar University (Girls’ Branch), Cairo 11651, Egypt
5
Department of Basic Sciences, Badr Institute of Science and Technology (BIS), Badr City 11829, Egypt
6
Department of Basic Sciences, Higher Institute of Marketing, Commerce & Information Systems (MCI), Cairo 11856, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(12), 2140; https://doi.org/10.3390/sym17122140
Submission received: 7 November 2025 / Revised: 25 November 2025 / Accepted: 1 December 2025 / Published: 12 December 2025
Versions Notes

Abstract

In recent years, there has been growing interest in discrete probability distributions due to their ability to model the complex behavior of real-world count data. In this paper, a new discrete mixture distribution based on two Weibull components is introduced, constructed using the general discretization approach. Several important statistical properties of the proposed distribution, including the survival function, hazard rate function, alternative hazard rate function, moments, quantile function, and order statistics are derived. It was concluded from the descriptive measures that the discrete mixture of two Weibull distributions transitions from being positively skewed with heavy tails to a more symmetric and light-tailed form. This demonstrates the high flexibility of the discrete mixture of two Weibull distributions in capturing a wide range of shapes as its parameter values vary. Estimation of the parameters is performed via maximum likelihood under Type II censoring scheme. A simulation study assesses the performance of the maximum likelihood estimators. Furthermore, the applicability of the proposed distribution is demonstrated using two real-life datasets. In summary, this paper constructs the discrete mixture of two Weibull distributions, investigates its statistical characteristics, and estimates its parameters, demonstrating its flexibility and practical applicability. These results highlight its potential as a powerful tool for modeling complex discrete data.
Keywords: discrete mixture of two Weibull components; survival function; hazard rate function; alternative hazard rate function; maximum likelihood method; Type-II censored samples; a simulation study discrete mixture of two Weibull components; survival function; hazard rate function; alternative hazard rate function; maximum likelihood method; Type-II censored samples; a simulation study

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MDPI and ACS Style

Salem, D.R.; Hegazy, M.A.; Mohammad, H.H.; Kalantan, Z.I.; AL-Dayian, G.R.; EL-Helbawy, A.A.; Abd Elaal, M.K. Advances in Discrete Lifetime Modeling: A Novel Discrete Weibull Mixture Distribution with Applications to Medical and Reliability Studies. Symmetry 2025, 17, 2140. https://doi.org/10.3390/sym17122140

AMA Style

Salem DR, Hegazy MA, Mohammad HH, Kalantan ZI, AL-Dayian GR, EL-Helbawy AA, Abd Elaal MK. Advances in Discrete Lifetime Modeling: A Novel Discrete Weibull Mixture Distribution with Applications to Medical and Reliability Studies. Symmetry. 2025; 17(12):2140. https://doi.org/10.3390/sym17122140

Chicago/Turabian Style

Salem, Doha R., Mai A. Hegazy, Hebatalla H. Mohammad, Zakiah I. Kalantan, Gannat R. AL-Dayian, Abeer A. EL-Helbawy, and Mervat K. Abd Elaal. 2025. "Advances in Discrete Lifetime Modeling: A Novel Discrete Weibull Mixture Distribution with Applications to Medical and Reliability Studies" Symmetry 17, no. 12: 2140. https://doi.org/10.3390/sym17122140

APA Style

Salem, D. R., Hegazy, M. A., Mohammad, H. H., Kalantan, Z. I., AL-Dayian, G. R., EL-Helbawy, A. A., & Abd Elaal, M. K. (2025). Advances in Discrete Lifetime Modeling: A Novel Discrete Weibull Mixture Distribution with Applications to Medical and Reliability Studies. Symmetry, 17(12), 2140. https://doi.org/10.3390/sym17122140

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