Record-Based Estimators for Weibull Distribution

Teimouri and Nadarajah [Statist. Methodol. 13 (2013) 12-24] considered bias corrected maximum likelihood estimation of the Weibull distribution based on upper record values. Here, we propose an estimator for the Weibull shape parameter based on consecutive upper records. It is shown by simulations that the proposed estimator has less bias and less mean squared error than an estimator due to Soliman et al. [Comput. Statist. Data Anal. 51 (2006) 2065-2077] based on all upper records. Also, the proposed estimator can be considered as a good competitor for the maximum likelihood estimator of the shape parameter based on complete data. This is proved by simulations and using a real dataset.