Marginalized Maximum Likelihood for Parameters Estimation of the Three Parameter Weibull Distribution

Abstract

The aims of this paper is to propose a new approach for fitting a three-parameter weibull distribution to data from an independent and identically distributed scheme of sampling. This approach use a likelihood function based on the n - 1 largest order statistics. Information loss by dropping the first order statistic is then retrieved via an MM-algorithm which will be used to estimate the model’s parameters. To examine the properties of the proposed estimators, the associated bias and mean squared error were calculated through Monte Carlo simulations. Subsequently, the performance of these estimators were compared with those of two concurrent methods.