Öz
Kaynakça
- [1] B. Abbasi, A. Jahromi, J. Arkat and M. Hosseinkouchack, Estimating the parameters of Weibull distribution using simulated annealing algorithm, Appl. Math. Comput. 183 (1), 85-93, 2006.
- [2] B. Abbasi, S. Niaki, M. Khalife and Y. Faize, Hybrid variable neighborhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution, Expert Syst. Appl. 38 (1), 700-708, 2011.
- [3] Ş. Acıtaş, Ç.H. Aladağ and B. Şenoğlu, A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data, Reliab. Eng. Syst. 183, 116-127, 2019.
- [4] B. Bergman, Estimation of Weibull parameters using a weight function, J. Mater. Sci. Lett. 5 (6), 611-614, 1986.
- [5] Y.K. Chu and J.C. Ke, Computation approaches for parameter estimation of Weibull distribution, Math. Comput. Appl. 17 (1), 39-47, 2012.
- [6] K.C. Datsiou and M. Overend, Weibull parameter estimation and goodness of fit for glass strength data, Struct. Saf. 73, 29-41, 2018.
- [7] I.J. Davies, Unbiased estimation of the Weibull scale parameter using linear least squares analysis, J. Eur. Ceram. Soc. 37 (8), 2973-2981, 2017.
- [8] K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms, John-Wiley and Sons, 2004.
- [9] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput. 6 (2), 182-197, 2002.
- [10] A. Hossain and H. Howlader, Unweighted least squares estimation of Weibull parameters, J. Stat. Comput. Simul. 54 (1-3), 265-271, 1996.
- [11] Y. Lei, Evaluation of three methods for estimating the Weibull distribution parameters of Chinese pine (Pinus tabulaeformis), J. For. Sci. 54 (12), 566-571, 2008.
- [12] R. Luus and M. Jammer, Estimation of parameters in 3-parameter Weibull probability distribution functions, Hung. J. Ind. Chem. 33 (1-2), 69-73, 2005.
- [13] D. Markovic, D. Jukic and M. Bensic, Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start, J. Comput. Appl. Math. 228 (1), 304-312, 2009.
- [14] M. Nassar, A.Z. Afify, S. Dey and D. Kumar, A new extension of Weibull distribution: Properties and different methods of estimation, J. Comput. Appl. Math. 336, 439-457, 2018.
- [15] H.H. Örkcü, V.S. Özsoy, E. Aksoy and M.. Doğan, Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison, Appl. Math. Comput. 268, 201-226, 2015.
- [16] I. Pobacikova and Z. Sedliackova, Comparison of four methods for estimating the Weibull distribution parameters, Appl. Math. Sci. 8 (83), 4137-4149, 2014.
- [17] M.L. Tiku and A.D. Akkaya, Robust Estimation and Hypothesis Testing, New Age International (P) Ltd. Publishers, 2004.
- [18] X.S. Yang, Engineering Optimization: An Introduction with Metaheuristic Applications, John Wiley and Sons, 2010.
Öz
Weibull distribution is widely used in various areas such as life tables, failure rates, and definition of wind speed distribution. Therefore, parameter estimation for the Weibull distribution is an important problem in many real data applications. The least square (LS), the weighted least square (WLS) and the maximum likelihood (ML) are the most popular methods for the parameter estimation in the Weibull distribution. In this study, based on the LS, WLS and ML estimation methods, a multi-objective programming approach is proposed for the parameter estimation of two-parameter Weibull distribution. This new approach evaluates together LS, WLS and ML methods in the estimation process. NSGA-II method, which is a multi-objective heuristic optimization method, is used to solve the proposed multi-objective estimation model. To evaluate the applicability and performance of the proposed approach, a detailed Monte Carlo simulation study based on deficiency criteria and a real data application are designed. The results illustrated that the proposed multi-objective programming approach provides quite accurate parameter estimates for the two parameter Weibull distribution with respect to deficiency criteria.
Anahtar Kelimeler
Weibull parameter estimation multi-objective programming NSGA-II
Kaynakça
- [1] B. Abbasi, A. Jahromi, J. Arkat and M. Hosseinkouchack, Estimating the parameters of Weibull distribution using simulated annealing algorithm, Appl. Math. Comput. 183 (1), 85-93, 2006.
- [2] B. Abbasi, S. Niaki, M. Khalife and Y. Faize, Hybrid variable neighborhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution, Expert Syst. Appl. 38 (1), 700-708, 2011.
- [3] Ş. Acıtaş, Ç.H. Aladağ and B. Şenoğlu, A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data, Reliab. Eng. Syst. 183, 116-127, 2019.
- [4] B. Bergman, Estimation of Weibull parameters using a weight function, J. Mater. Sci. Lett. 5 (6), 611-614, 1986.
- [5] Y.K. Chu and J.C. Ke, Computation approaches for parameter estimation of Weibull distribution, Math. Comput. Appl. 17 (1), 39-47, 2012.
- [6] K.C. Datsiou and M. Overend, Weibull parameter estimation and goodness of fit for glass strength data, Struct. Saf. 73, 29-41, 2018.
- [7] I.J. Davies, Unbiased estimation of the Weibull scale parameter using linear least squares analysis, J. Eur. Ceram. Soc. 37 (8), 2973-2981, 2017.
- [8] K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms, John-Wiley and Sons, 2004.
- [9] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput. 6 (2), 182-197, 2002.
- [10] A. Hossain and H. Howlader, Unweighted least squares estimation of Weibull parameters, J. Stat. Comput. Simul. 54 (1-3), 265-271, 1996.
- [11] Y. Lei, Evaluation of three methods for estimating the Weibull distribution parameters of Chinese pine (Pinus tabulaeformis), J. For. Sci. 54 (12), 566-571, 2008.
- [12] R. Luus and M. Jammer, Estimation of parameters in 3-parameter Weibull probability distribution functions, Hung. J. Ind. Chem. 33 (1-2), 69-73, 2005.
- [13] D. Markovic, D. Jukic and M. Bensic, Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start, J. Comput. Appl. Math. 228 (1), 304-312, 2009.
- [14] M. Nassar, A.Z. Afify, S. Dey and D. Kumar, A new extension of Weibull distribution: Properties and different methods of estimation, J. Comput. Appl. Math. 336, 439-457, 2018.
- [15] H.H. Örkcü, V.S. Özsoy, E. Aksoy and M.. Doğan, Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison, Appl. Math. Comput. 268, 201-226, 2015.
- [16] I. Pobacikova and Z. Sedliackova, Comparison of four methods for estimating the Weibull distribution parameters, Appl. Math. Sci. 8 (83), 4137-4149, 2014.
- [17] M.L. Tiku and A.D. Akkaya, Robust Estimation and Hypothesis Testing, New Age International (P) Ltd. Publishers, 2004.
- [18] X.S. Yang, Engineering Optimization: An Introduction with Metaheuristic Applications, John Wiley and Sons, 2010.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | İstatistik |
| Bölüm | İstatistik |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Nisan 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 51 Sayı: 2 |