Estimating the Parameters of the Three-Parameter Lognormal Distribution

Authors

Rodrigo J. Aristizabal, Florida International UniversityFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

Zhenmin Chen

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Gauri L. Ghai

Second Advisor's Committee Title

Committee Co-Chair

Third Advisor's Name

Florence George

Keywords

Estimating Parameters, Three-Parameter Lognormal Distribution

Date of Defense

3-30-2012

Abstract

The three-parameter lognormal distribution is widely used in many areas of science. 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 encounters multiple estimates.

The purpose of this research is focused on estimating the threshold or location parameter , because when is known, then 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, and SAS/IML were used to accomplish this objective. The bias of the point estimator and mean square error (MSE) criteria were used throughout extensive simulation to evaluate the performance of the proposed method. The result shows that the proposed method can provide quite accurate estimates.

Identifier

FI12042308

Recommended Citation

Aristizabal, Rodrigo J., "Estimating the Parameters of the Three-Parameter Lognormal Distribution" (2012). FIU Electronic Theses and Dissertations. 575.
https://digitalcommons.fiu.edu/etd/575