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MLE of Three-Parameter Weibull Distribution in Multi-Data Types

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Abstract:

An algorithm is presented for maximum likelihood estimation (MLE) of three-parameter Weibull distribution in this paper, which is not only suitable for uncensored data but also appropriate for various censored data. Firstly, a unified likelihood equation under censored data and uncensored data was built. Here, the second-order convergent Newton-Raphson iteration method was applied to solve the MLE of two-parameter Weibull distribution, which had only scale parameter and shape parameter with a given positional parameter. Then, the steady and rapid Brent search method was applied to solve the optimal solution of the likelihood function just with a single variable of positional parameter. Finally, several examples were given to demonstrate the stability and efficiency of this algorithm.

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Info:

Periodical:

Advanced Materials Research (Volume 145)

Pages:

37-42

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.145.37

Citation:

Cite this paper

Online since:

October 2010

Authors:

Yu Jin Wang, Ying Fan, Shun Kun Wang

Keywords:

Brent Search Method, Censored Data, Maximum Likelihood-Estimation (MLE), Newton-Raphson Iteration Method, Three-Parameter Weibull Distribution

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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References

[1] M.C. Yang, H. Nie: Advanced algorithm for maximum likelihood estimation of three-parameter weibull distribution. Journal of Nanjing University of Aeronautics & Astronautic, Vol. 29 (2007) p.23. (In Chinese).

Google Scholar

[2] X.H. Yu, L.B. Zhang, C.H. Wang and L.X. Duan: Reliability life analysis of the equipment based on new weibull distribution parameter estimation method. Journal of Mechanical Strength, Vol. 29 (2007), p.932. (In Chinese).

Google Scholar

[3] H.S. Wang, Z.H. Li and R.W. Lin: Maximum Likelihood estimation for three-parameter Weibull distribution based on wear out fault. China Railway Scienc, Vol. 25 (2004) No. 5, p.40. (In Chinese).

Google Scholar

[4] Balakrishnana N, Katerib M: On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data. Statistics & Probability Letters, Vol. 78 (2008) No. 12, p.2971.

DOI: 10.1016/j.spl.2008.05.019

Google Scholar

[5] J.Z. Shi, X.Z. Yang and X.C. Chen: Comparative study on parameter estimation methods for 3-parameter Weibull distribution. Journal of Henan Agricultural University, Vol. 43 (2009) No. 8, p.405. (In Chinese).

Google Scholar

[6] K.L. ZHOU, Y.H. KANG: Neural network model and simulation programming in MATLAB (Tsinghua University Press, China 2005) . (In Chinese).

Google Scholar

[7] Y.G. Wu, J. Zhou, Z. Wang and Y. Zeng: Parameter estimation of Weibull distribution using the EM algorithm based on randomly censored data. Journal of Sichuan University: Natural Science Edition, Vol. 42 (2005) No. 5, p.910. (In Chinese).

Google Scholar