Modified Moment Estimation for the Three-Parameter Lognormal Distribution

Abstract

A modification of moment estimators in which the third moment is replaced by a function of the first order statistic is presented for parameters of the three-parameter lognormal distribution. The modified estimators enjoy advantages over traditional moment estimators with respect to both bias and variance. With the aid of accompanying tables and charts, they are much easier to calculate than local maximum likelihood estimators, and their bias and variance are near minimal. Unlike maximum likelihood estimators which introduce various regularity and existence problems, the modified estimators are applicable over the entire parameter space and existence problems do not arise. Two illustrative examples are included.