Accession Number : ADA138007

Title :   Robust Minimum Distance Estimation of the Three Parameter Lognormal Distribution.

Descriptive Note : Master's thesis,


Personal Author(s) : Keffer,J H

PDF Url : ADA138007

Report Date : Dec 1983

Pagination or Media Count : 116

Abstract : This thesis compares two modified maximum likelihood (ML) estimation techniques against three minimum distance (MD) estimation techniques in application to the three parameter lognormal distribution. The three parameter lognormal distribution has a location parameter (xi) and two other parameters associated with the mean (micron) and standard deviation (delta) of its parent normal population. The first modified ML technique uses linear interpolation on order statistics to estimate location while the second ML technique uses the first order statistic as the location estimate. The remaining two parameters are calculated by using the location estimate in their respective censored or uncensored ML equations and solving for the parameters. Three MD techniques are used: Kolmogrov Distance, Cramer-von Mises Statistic, and the Anderson-Darling Statistic. The MD techniques refine the location estimates which are then used in the ML equations of the other two parameters to obtain their refined estimates. Monte Carlo analysis is used to accomplish the comparison of estimation techniques. Three measures of effectiveness are used to facilitate comparisons: mean square error, relative efficiency, and the Cramer-von Mises Statistic. Comparisons of these effectiveness measures across all cases reveal a clear superiority of the MD techniques over the modified ML techniques. (Author)

Descriptors :   *Statistical analysis, *Estimates, *Maximum likelihood estimation, Comparison, Computer programs, Parameters, Distribution functions, Order statistics, Monte Carlo method, Interpolation, Military applications, Standard deviation, Theses

Subject Categories : Statistics and Probability
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE