Interval and point estimators for the location parameter of the three-parameter lognormal distribution (Q1953811)

Summary: The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the needs of the biological, sociological, and other fields. Numerous research papers have been published on the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation results show that the proposed method is less biased in estimating the location parameter. The large sample size case is alsor.