Estimation of Weibull distribution parameters using a genetic algorithm

Document Type : Original Article

Authors

1 Department of Statistics, Imam Khomeini International University, Qazvin, Iran.

2 Department of Applied Mathematics, Imam Khomeini International University, Qazvin, Iran.

Abstract
Purpose: This paper aims to estimate the parameters of the Weibull distribution using a genetic algorithm and compare its performance with traditional estimation methods.
Methodology: A simulation study was conducted under different sample sizes and censoring levels. The genetic algorithm was applied to maximize the likelihood function.
Findings: The results show that the genetic algorithm provides more accurate and stable parameter estimates compared to the maximum likelihood method, especially in the presence of censored data.
Originality/Value: This study presents a novel application of genetic algorithms in reliability analysis, demonstrating their effectiveness in parameter estimation for censored datasets.

Keywords

Subjects

[1]    Klein, J. P., & Moeschberger, M. L. (2006). Multivariate survival analysis. In Survival analysis: techniques for censored and truncated data (pp. 425–441). Springer. https://doi.org/10.1007/0-387-21645-6_13
[2]    Dodson, B. (2006). The Weibull analysis handbook. ASQ Quality Press. https://cir.nii.ac.jp/crid/1971993809695576965
[3]    Kececioglu, D. B., & Wang, W. (1998). Parameter estimation for mixed-weibull distribution. Annual reliability and maintainability symposium. 1998 proceedings. international symposium on product quality and integrity (pp. 247–252). IEEE. https://doi.org/10.1109/RAMS.1998.653782
[4]    Lakshmi, R. V., & Vaidyanathan, V. S. (2016). Parameter estimation in gamma mixture model using normal-based approximation. Journal of statistical theory and applications, 15(1), 25–35. https://doi.org/10.2991/jsta.2014.13.3.1
[5]    Elmahdy, E. E., & Aboutahoun, A. W. (2013). A new approach for parameter estimation of finite Weibull mixture distributions for reliability modeling. Applied mathematical modelling, 37(4), 1800–1810. https://doi.org/10.1080/02664763.2014.1000275
[6]    Kaled, H. R., José, L. R., Vega, E., Becerra-Rozas, M., & Andrés, R. (2025). Robust metaheuristic optimization for algorithmic trading: A comparative study of optimization techniques. Mathematics, 14(1), 69. https://doi.org/10.3390/math14010069
[7]    Yan, T., Fang, K. T., & Yin, H. (2024). A novel approach for parameter estimation of mixture of two Weibull distributions in failure data modeling. Statistics and computing, 34(6), 221. https://doi.org/10.1007/s11222-024-10534-1
[8]    Jokiel-Rokita, A., & Pia̧tek, S. (2024). Estimation of parameters and quantiles of the Weibull distribution. Statistical papers, 65(1), 1–18. https://doi.org/10.1007/s00362-022-01379-9
[9]    Karakoca, A., Erisoglu, U., & Erisoglu, M. (2015). A comparison of the parameter estimation methods for bimodal mixture Weibull distribution with complete data. Journal of applied statistics, 42(7), 1472–1489. https://doi.org/10.1080/02664763.2014.1000275
[10] Holland, J. (1975). Adaptation in natural and artificial systems. University of Michigan Press, ann arbor. https://books.google.com/books/about/Adaptation_in_Natural_and_Artificial_Sys.html?id=JE5RAAAAMAAJ
[11] Alhijawi, B., & Awajan, A. (2024). Genetic algorithms: Theory, genetic operators, solutions, and applications. Evolutionary intelligence, 17(3), 1245–1256. https://doi.org/10.1007/s12065-023-00822-6
[12] Wolpert, D. H., & Macready, W. G. (2002). No free lunch theorems for optimization. IEEE transactions on evolutionary computation, 1(1), 67–82. https://doi.org/10.1109/4235.585893
[13] Katoch, S., Chauhan, S. S., & Kumar, V. (2021). A review on genetic algorithm: Past, present, and future. Multimedia tools and applications, 80, 8091–8126. https://link.springer.com/article/10.1007/s11042-020-10139-6
[14] Deb, K. (2001). Multi-objective optimization using evolutionary algorithms John Wiley & Sons. John Wiley & Sons. https://www.wiley.com/en-us/Multi-Objective+Optimization+using+Evolutionary+Algorithms-p-9780471873396
[15] Alexakis, K., Benekis, V., Kokkinakos, P., & Askounis, D. (2025). Genetic algorithm-based multi-objective optimisation for energy-efficient building retrofitting: A systematic review. Energy and buildings, 328, 115216. https://doi.org/10.1016/j.enbuild.2024.115216
[16] Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the royal statistical society: series b (methodological), 39(1), 1–22. https://doi.org/10.1111/j.2517-6161.1977.tb01600.x
[17] McLachlan, G. J., & Krishnan, T. (2008). The EM algorithm and extensions. John Wiley & Sons. https://www.wiley.com/en-br/The+EM+Algorithm+and+Extensions%2C+2nd+Edition-p-9780471201700
[18] Tekeli, E., & Yüksel, G. (2022). Estimating the parameters of twofold Weibull mixture model in right-censored reliability data by using genetic algorithm. Communications in statistics-simulation and computation, 51(11), 6621–6634. https://doi.org/10.1080/03610918.2020.1808681