Estimation Using Quantile Function Structure with Emphasis on Weibull Distribution

An approach to estimation of parameters of quantile function models is proposed and applied to constructing simple L-estimators of the parameters of the Weibull models. The general approach to construction involves starting with convenient pivotal statistics and refining them using the jackknife method to obtain simple closed form estimators. Empirical studies of these closed form L-estimators for the Weibull parameters so obtained show that they are essentially bias free and in terms of MSE compare very well with the MLE and other competitors.