Standard and goodness-of-fit parameter estimation methods for the three-parameter lognormal distribution

Abstract

A class of goodness-of-fit estimators is found to provide a useful alternative in certain situations to the standard maximum likelihood method which has some undesirable estimation characteristics for estimation from the three-parameter lognormal distribution. The class of goodness-of-fit tests considered include the Shapiro-Wilk and Filliben tests which reduce to a weighted linear combination of the order statistics that can be maximized in estimation problems. The weighted order statistic estimators are compared to the standard procedures in Monte Carlo simulations. Robustness of the procedures are examined and example data sets analyzed.

Keywords:

• lognormal distribution
• three-parameter lognormal distribution
• weighted order statistic estimation
• Shapiro-Franoia test
• local maximum likelihood estimation