Efficient and Robust Fitting of Lognormal Distributions

Abstract

In parametric modeling of loss distributions in actuarial science, a versatile choice with intermediate tail weight is the lognormal distribution. Surprisingly, however, the fitting of this model using estimators that are at once efficient and robust has not been seriously addressed in the extensive literature. Consequently, typical estimators of the lognormal mean and variance fail to be both efficient and robust. In particular, the highly efficient maximum likelihood estimators lack robustness because of their limited sensitivity to outliers in the sample. For the two-parameter lognormal estimation problem, the author considers the problem of efficient and robust joint estimation of the mean and variance of a normal model. He introduces generalized-median-type estimators that yield efficient and robust estimators of various parameters of interest in the lognormal model. The paper provides detailed treatment of the lognormal mean and discusses extension of the approach to the much more complicated problem of estimation for the three-parameter lognormal model.