Interval Estimation for the Three‐Parameter Lognormal Distribution Via the Likelihood Function

There is a substantial literature on estimation for the three‐parameter lognormal distribution {ln(Y— γ)~ N(μ, σ2)}. A large variety of estimators has been developed. The emphasis placed on alternative techniques by some of these authors is substantially due to the fact that the method of maximum likelihood has wrongly been discredited because of supposed computational difficulties and theoretical uncertainties. The literature has concentrated on point estimation with scant attention being paid to interval estimates. It is the purpose of this note to show how the interval estimation problem may be examined via the likelihood function. A comparison of these likelihood intervals, approximate and exact confidence intervals is made. Graphical examination of the likelihood function also presents a simple way of overcoming computational difficulties in obtaining point estimates (and shows why they arise), enabling a thorough examination of the information contained in the data about the model parameters and suggesting stable parameter transformations.