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On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data

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  • Balakrishnan, N.
  • Kateri, M.

Abstract

The estimation of parameters of a Weibull distribution, requiring numerical methods, has been discussed by numerous authors. In this paper, an alternative approach based on a very simple and easy-to-apply graphical method is proposed, which also readily shows the existence and uniqueness of the maximum likelihood estimates. Furthermore, for censored data from a large sample size, a closed-form estimator for the shape parameter is also obtained.

Suggested Citation

  • Balakrishnan, N. & Kateri, M., 2008. "On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2971-2975, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2971-2975
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    1. Coria, V.H. & Maximov, S. & Rivas-Dávalos, F. & Melchor, C.L. & Guardado, J.L., 2015. "Analytical method for optimization of maintenance policy based on available system failure data," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 55-63.
    2. Pareek, Bhuvanesh & Kundu, Debasis & Kumar, Sumit, 2009. "On progressively censored competing risks data for Weibull distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4083-4094, October.
    3. Marcus Johnen & Stefan Bedbur & Udo Kamps, 2020. "A note on multiple roots of a likelihood equation for Weibull sequential order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 519-525, May.
    4. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    5. Muqrin A. Almuqrin & Mukhtar M. Salah & Essam A. Ahmed, 2022. "Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications," Mathematics, MDPI, vol. 10(22), pages 1-38, November.
    6. Benjamin Laumen & Erhard Cramer, 2021. "k‐step stage life testing," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 203-233, May.
    7. Joseph Y. J. Chow & Hamid R. Sayarshad, 2016. "Reference Policies for Non-myopic Sequential Network Design and Timing Problems," Networks and Spatial Economics, Springer, vol. 16(4), pages 1183-1209, December.
    8. Tzong-Ru Tsai & Yuhlong Lio & Jyun-You Chiang & Yi-Jia Huang, 2022. "A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme," Mathematics, MDPI, vol. 10(21), pages 1-17, November.
    9. Jarosław Piątkowski & Bożena Gajdzik & Aleksander Mesjasz, 2020. "Assessment of Material Durability of Steam Pipelines Based on Statistical Analysis of Strength Properties—Selected Models," Energies, MDPI, vol. 13(14), pages 1-18, July.
    10. Farha Sultana & Yogesh Mani Tripathi & Shuo-Jye Wu & Tanmay Sen, 2022. "Inference for Kumaraswamy Distribution Based on Type I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 9(6), pages 1283-1307, December.
    11. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    12. Katopodis, Theodoros & Markantonis, Iason & Vlachogiannis, Diamando & Politi, Nadia & Sfetsos, Athanasios, 2021. "Assessing climate change impacts on wind characteristics in Greece through high resolution regional climate modelling," Renewable Energy, Elsevier, vol. 179(C), pages 427-444.
    13. Ritwik Bhattacharya, 2020. "Implementation of compound optimal design strategy in censored life-testing experiment," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1029-1050, December.
    14. Ahmed Soliman & N. Abou-elheggag & A. Abd ellah & A. Modhesh, 2012. "Bayesian and non-Bayesian inferences of the Burr-XII distribution for progressive first-failure censored data," METRON, Springer;Sapienza Università di Roma, vol. 70(1), pages 1-25, April.
    15. Nagatsuka, Hideki & Kamakura, Toshinari & Balakrishnan, N., 2013. "A consistent method of estimation for the three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 210-226.
    16. Benjamin Laumen & Erhard Cramer, 2019. "Stage life testing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 632-647, December.
    17. Wang, Liang & Tripathi, Yogesh Mani & Lodhi, Chandrakant & Zuo, Xuanjia, 2022. "Inference for constant-stress Weibull competing risks model under generalized progressive hybrid censoring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 70-83.
    18. Francesco Corman & Sander Kraijema & Milinko Godjevac & Gabriel Lodewijks, 2017. "Optimizing preventive maintenance policy: A data-driven application for a light rail braking system," Journal of Risk and Reliability, , vol. 231(5), pages 534-545, October.
    19. Bucher, Axel & Segers, Johan, 2015. "Maximum likelihood estimation for the Frechet distribution based on block maxima extracted from a time series," LIDAM Discussion Papers ISBA 2015023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Arthur H.A. Melani & Carlos A. Murad & Adherbal Caminada Netto & Gilberto F.M. Souza & Silvio I. Nabeta, 2019. "Maintenance Strategy Optimization of a Coal-Fired Power Plant Cooling Tower through Generalized Stochastic Petri Nets," Energies, MDPI, vol. 12(10), pages 1-28, May.

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