A consistent method of estimation for the three-parameter Weibull distribution
In this paper, we propose a new method for the estimation of parameters of the three-parameter Weibull distribution. The method is based on a data transformation, which avoids the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely in the entire parameter space, and the estimators also have consistency over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method performs better than some existing methods in terms of bias and root mean squared error (RMSE). Finally, two examples based on real data sets are presented to illustrate the proposed method.
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Volume (Year): 58 (2013)
Issue (Month): C ()
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- 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.
- Jukic, Dragan & Bensic, Mirta & Scitovski, Rudolf, 2008. "On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4502-4511, May.
- Peter Hall & Julian Z. Wang, 2005. "Bayesian likelihood methods for estimating the end point of a distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 717-729.
- Castillo, Enrique & Hadi, Ali S., 1995. "A method for estimating parameters and quantiles of distributions of continuous random variables," Computational Statistics & Data Analysis, Elsevier, vol. 20(4), pages 421-439, October.
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