A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter

Nine parametric estimators of the location and scale parameters of a two-parameter Weibull distribution are compared in terms of their bias and efficiency in a simulation study. The estimators considered are the maximum likelihood estimators (MLE), moment estimators (ME), generalized spacing estimators (GSE), modified maximum likelihood estimators I (MMLE-I), modified maximum likelihood estimators II (MMLE-II), Tiku's modified maximum likelihood estimators (TMMLE), least-squares estimators (LSE), weighted least-squares estimators (WLSE) and percentile estimators (PCE). The aim of the comparisons is to identify the most efficient estimators among these nine estimators for different shape parameters and sample sizes.