PARAMETER ESTIMATION BASED ON MAXIMUM LIKELIHOOD ESTIMATION METHOD FOR WEIBULL DISTRIBUTION USING DRAGONFLY ALGORITHM

Abstract

Three-parameter (3-p) Weibull distribution is commonly used in sciences such as engineering, reliability, and renewable energy. Thus, a great number of studies have been conducted on the estimation for the parameters of this distribution. One of the mostly utilized methods for estimating the unknown parameters of the Weibull distribution in the related literature is Maximum likelihood (ML) method. In this study, a population-based novel heuristic method is proposed to use the Dragonfly Algorithm (DA) for obtaining the Maximum Likelihood estimates of three-parameter Weibull distribution. Inspired by the static and dynamic swarming behavior of the dragonflies in nature, Dragonfly algorithm has been introduced. These behaviors ensure that the algorithm has a high exploration and exploitation. An extensive Monte-Carlo simulation study is conducted to show the performance of the DA. Furthermore, the performance of DA is compared with other algorithms well known in the literature. Finally, a real data set is analyzed to show the applicability of the ML estimation based on the DA.

Keywords

• Dragonfly Algorithm
• Maximum Likelihood Estimation
• Monte Carlo Simulation
• Weibull Distribution.

References

1. Weibull, W., A statistical theory of strength of materials, Stockholm: Generalstabens litografiska anstalts förlag, 1939.
2. Nagatsuka, H., Kamakura, T. and Balakrishnan, N., "A consistent method of estimation for the three-parameter Weibull distribution", Computational Statistics Data Analysis”, 58, 210-226, 2013.
3. Almalki, S. J., and Nadarajah, S., “Modifications of the Weibull distribution: A review”, Reliability Engineering System Safety, 124, 32-55, 2014.
4. Johnson N.L., Kotz S. and Balakrishnan N., Univariate continuous distributions: New York: John Wiley & Sons, 1994. Yonar, A., Metaheuristic approaches for estimating parameters of univariate and multivariate distributions, PhD thesis, Selçuk University: Konya,Turkey, 2020.
5. Abbasi B., Jahromi A.H.E., Arkat J. and Hosseinkouchack M., "Estimating the parameters of Weibull distribution using simulated annealing algorithm", Applied Mathematics and Computation 183, 1, 85-93, 2006.
6. Abbasi B., Niaki S.T.A., Khalife M.A. and Faize Y., " A hybrid variable neighborhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution", Expert Systems with Applications, 38, 1, 700-708, 2011.
7. Örkcü H., Aksoy E. and Dogan M.İ., "Estimating the parameters of 3-p Weibull distribution through differential evolution", Applied Mathematics and Computation 251, 211-224, 2015.
8. Örkcü H., Özsoy V.S., Aksoy E. and Dogan M.I., "Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison" , Applied Mathematics and Computation, 268, 201-226, 2015.

9. Carneiro, T. C., Melo, S. P., Carvalho, P. C., & Braga, A. P. D. S., “Particle swarm optimization method for estimation of Weibull parameters: a case study for the Brazilian northeast region”. Renewable energy, 86, 751-759, 2016.
10. Yang F., Ren H. and Hu Z. , "Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy", Mathematical Problems in Engineering, Article ID 6281781, 2019.
11. Acitas S., Aladag C.H. and Senoglu B., "A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data Reliability, Engineering System Safety, 183, 116-127, 2019.
12. Yonar, A. and Pehlivan, N. Y., "Artificial bee colony with levy flights for parameter estimation of 3-p weibull distribution", Iranian Journal Science and Technology, Transaction A, 44, 3, 851-864, 2020.
13. Mirjalili S., "Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems", Neural Computing Applications, 27, 4, 1053-1073, 2016.
14. Yalçınkaya A., Şenoğlu B. and Yolcu U., "Maximum likelihood estimation for the parameters of skew normal distribution using genetic algorithm", Swarm and Evolutionary Computation, 38, 127-138, 2018.
15. Murthy D., Xie M. and Jiang R., Weibull models, John Wiley, New York, 2004.