Approximation to the Mean and Variance of the Modified Moments Estimator of the Shape Parameter of Weibull Distribution

Abstract

In this paper we consider the Weibull distribution of two parameters , since has been widely used as a model in many areas of applications. Properties of the distribution are introduced . Estimation of the distribution parameters is obtained by the modified moments method. The estimator of the shape parameter has so complicated form and it is difficult to find the properties of estimator so approximation to the mean and variance of the estimator is made theoretically by utilizing Taylor series expansion up to second order derivative.