On A Closed-Form Estimator of the Shape Parameter of the Three-Parameter Weibull Distribution (Published)
The shape parameter of the three-parameter Weibull distribution () was considered in this study. Known estimation methods like the maximum likelihood, method of moment and maximum product of spacing do not have closed-form estimators for the shape parameter of the three-parameter Weibull distribution rather they involve iterative procedures which may be time-consuming and are less tractable. Dubey (1967), Goda et al (2010) and Teimouri and Gupta (2013) have proposed closed-form estimators for . In this study, a closed-form estimator for is proposed and the proposed estimator is compared with the existing closed-form estimators proposed by the authors mentioned above. To compare the accuracy of the estimators, Monte Carlo simulation is performed. Simulated data from the Weibull distribution are used to check the accuracy of the estimators and the root mean square error (RMSE) is used as a metric for accuracy. The results show that in general, the proposed estimator performs better than the other three closed-form estimators that were compared.
Keywords: Accuracy, Estimators, Parameter, tractability, weibull