Abstract
The likelihood function is modified substituting the empirical distribution by a kernel estimator. The parametric estimate that is deduced by maximizing the modified likelihood has only a bias of order o(l/n) under certain conditions. Thus the bias of Maxi¬mum Likelihood Estimates is reduced. A modified version of the Maximum Likelihood Estimator of the shape parameter of the Weibuii distribution is studied as well for un-censored samples as for censored ones