The Infeasibility of Probability Weighted Moments Estimation of Some Generalized Distributions

The method of probability weighted moments is a very useful method for estimating parameters of continuous distributions. Its good robust property, small bias and rapid convergence to the normal distribution, all make this method attractive. However, when estimating the parameters of some generalized distributions, such as the generalized extreme value, Pareto and logistic distributions, the method of probability weighted moments can lead to infeasible estimates in the sense that the estimated distribution has an upper or lower bound and one or more of the data values lie outside this bound. In this paper, we investigate the infeasibility of the parameter estimates obtained by the method of probability weighted moments for the parameters of the above mentioned generalized distributions.