title: Two-step estimators of the scale parameter of the Weibull distribution.
abstract: An efficient two-step method of estimating the scale parameter of the Weibull distribution is presented and compared to other estimation procedures. The shape parameter is obtained by a procedure other than maximum likelihood and then substituted into the maximum likelihood formula for the scale parameter. Three two-step and four one-step estimators were compared using a Monte Carlo simulation. When the shape parameter is less than one, the two-step estimator using a generalized least-squares estimate of the shape parameter was best in terms of observed relative efficiency. Maximum likelihood was best, but followed closely by the generalized least-squares estimator when the shape parameter is greater than one.
mesh_terms: D001699:Biometry; D009010:Monte Carlo Method