Estimating Parameters of the Three-parameter Lognormal Distribution: Focusing on the Threshold or Location Parameter

The three-parameter lognormal distribution is widely used in many areas of sciences. Some modifications have been proposed to improve the maximum likelihood estimator. In some cases, however, the modified maximum likelihood estimates do not exist or the procedure encounter multiple estimates. The purpose of this research is focused on estimating the threshold or location parameter,because the other two estimated parameters are obtained from the first two MLE equations. In this research, a method for constructing confidence intervals, confidence limits, and point estimator for the threshold parameter is proposed. Monte-Carlo simulation, bisection method, SAS/IML, bias of point estimator and mean square error (MSE) criteria were used throughout extensive simulation to evaluated the performance of the proposed method. The results shows that the proposed method can provide quite accurate estimates.