A Comparison of Methods for the Estimation of two-parameter Weibull Distribution with Outlier

Main Article Content

Kanlaya Boonlha


 In this study, we compare the three different methods for the joint estimation of both scale and shape parameters for two-parameter in Weibull distribution when data are contaminated with outliers: the method of moment (MOM), the maximum likelihood method (MLE) and the weighted likelihood method (WLE). The performance of these methods is compared using the Monte Carlo s imulation and the efficiency of these methods is compared based on RMSE. From simulation results, we found that the WLE outperforms the other methods for the scale parameter in term of RMSE of the estimator for scale parameter for gif.latex?\beta&space;=&space;0.5. For the RMSE of the estimator for shape parameter of the MLE approach provides better results for the scale parameter when outliers in the data set are small. In term of RMSE for two parameter estimators, the WLE performs better than the other methods when gif.latex?\beta&space;=&space;0.5. For gif.latex?\beta&space;=&space;1 and 1.5, the MOM also performs well, especially and outliers in the data set are small.

Article Details



Ahmed, E. S., Volodin, A. I., & Hussein, A. A. (2005). Robust weighted likelihood estimation of

exponential parameters. Reliability, IEEE Transactions on, 54(3), 389-395. DOI:


Boonlha. K.(2013). The weighted likelihood estimator of scale parameter for two-

parameter weibull distribution with contamination. Thesis, Thammasart University

Boudt, K., Caliskan, D., & Croux, C. (2011). Robust explicit estimators of Weibull parameters.

Metrika, 73(2), 187-209. DOI: 10.1007/s00184-009-0272-1

Hu, F. (1997). The asymptotic properties of the maximum relevance weighted likelihood

estimators. Canadian Journal of Statistics, 25(1), 45-59.

Hu, F., & Zidek, J. V. (2001). The relevance weighted likelihood with applications. In

Empirical Bayes and Likelihood Inference. (pp. 211-235). Springer New York.

R Development Core team.,(2013). R:Language and Environment for Statistical and

computing. Available at: http://www.R-project.org, accessed March 14,2013.