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Year 2022, Volume: 51 Issue: 2, 543 - 558, 01.04.2022

Emre Koçak Ecem Demir Yurtseven H. Hasan Örkcü

https://doi.org/10.15672/hujms.912435

Abstract

References

  • [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.

A multi-objective programming approach to Weibull parameter estimation

Year 2022, Volume: 51 Issue: 2, 543 - 558, 01.04.2022

Emre Koçak Ecem Demir Yurtseven H. Hasan Örkcü

https://doi.org/10.15672/hujms.912435

Abstract

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.

Keywords

Weibull parameter estimation multi-objective programming NSGA-II

References

  • [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.
There are 18 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Emre Koçak 0000-0001-6686-9671

Ecem Demir Yurtseven 0000-0001-9714-0672

H. Hasan Örkcü 0000-0002-2888-9580

Publication Date April 1, 2022
Published in Issue Year 2022 Volume: 51 Issue: 2

Cite

APA Koçak, E., Demir Yurtseven, E., & Örkcü, H. H. (2022). A multi-objective programming approach to Weibull parameter estimation. Hacettepe Journal of Mathematics and Statistics, 51(2), 543-558. https://doi.org/10.15672/hujms.912435
AMA Koçak E, Demir Yurtseven E, Örkcü HH. A multi-objective programming approach to Weibull parameter estimation. Hacettepe Journal of Mathematics and Statistics. April 2022;51(2):543-558. doi:10.15672/hujms.912435
Chicago Koçak, Emre, Ecem Demir Yurtseven, and H. Hasan Örkcü. “A Multi-Objective Programming Approach to Weibull Parameter Estimation”. Hacettepe Journal of Mathematics and Statistics 51, no. 2 (April 2022): 543-58. https://doi.org/10.15672/hujms.912435.
EndNote Koçak E, Demir Yurtseven E, Örkcü HH (April 1, 2022) A multi-objective programming approach to Weibull parameter estimation. Hacettepe Journal of Mathematics and Statistics 51 2 543–558.
IEEE E. Koçak, E. Demir Yurtseven, and H. H. Örkcü, “A multi-objective programming approach to Weibull parameter estimation”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 2, pp. 543–558, 2022, doi: 10.15672/hujms.912435.
ISNAD Koçak, Emre et al. “A Multi-Objective Programming Approach to Weibull Parameter Estimation”. Hacettepe Journal of Mathematics and Statistics 51/2 (April 2022), 543-558. https://doi.org/10.15672/hujms.912435.
JAMA Koçak E, Demir Yurtseven E, Örkcü HH. A multi-objective programming approach to Weibull parameter estimation. Hacettepe Journal of Mathematics and Statistics. 2022;51:543–558.
MLA Koçak, Emre et al. “A Multi-Objective Programming Approach to Weibull Parameter Estimation”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 2, 2022, pp. 543-58, doi:10.15672/hujms.912435.
Vancouver Koçak E, Demir Yurtseven E, Örkcü HH. A multi-objective programming approach to Weibull parameter estimation. Hacettepe Journal of Mathematics and Statistics. 2022;51(2):543-58.

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