In parametric modeling of loss distributions in actuarial science, a versatile choice with intermediate tail weight is the lognormal distribution. This 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. At the end of this paper, there is a discussion between author and Thierry Duchesne and Jacques Rioux. From NAAJ, October 2002, Volume 6, Number 4.