Estimator for the Parameters of the Weibull Distribution Based on Complete Sample

Consider the Weibull distribution with scale parameter θ and shape parameter β. In this paper, discuss the properties of moment-type estimators \widehat\theta and \widehat\beta of θ and β for complete sample, and compare \widehat\theta and \widehat\beta with simple linear unbiased estimators ~θ and ~β of θ and β. Strong consistency and asymptotic normality of \widehat\theta and \widehat\beta, which can be computed easily, are proved. Some simulation results are also given.