Abstract
The three-parameter log-elliptical distribution class is developed for the general situation in which the hypothesis of independence for the elements in a sample is not assumed. The parameter estimators are theoretically showed to be invariant under all distributions in the class by considering only a change in the constant of the scale parameter estimator. An estimation procedure based on the three-parameter lognormal distribution is proposed for the parameter estimation problem in any three-parameter log-elliptical distribution. Two classical lognormal data sets are analyzed without assuming independence in the sample in order to illustrate the proposed estimation procedure.
Mathematics Subject Classification:
Acknowledgments
This research work was partially supported by CONACYT-México, research grant no. 81512 and IDI-Spain, grants FQM2006-2271 and MTM2008-05785. This article was written during J. A. Díaz- García's stay as a visiting professor at the Department of Statistics and O. R. of the University of Granada, Spain. The authors wish to thank the Associate Editor and anonymous reviewers for their constructive comments on the preliminary version of this article.
Notes
The independent case is currently under consideration.
The programs and data sets are available upon request.