Generalized elliptical distributions

ABSTRACT

A family of distributions generated by an operator acting on generalized normal density is introduced. This family contains as particular cases many known distributions, including the generalized normal, generalized t, and generalized gamma distributions. Several mathematical properties of the family (including expansions, characteristic function, moments, cumulants, and order statistics properties) are derived. Estimation procedures are derived too by the method of moments, method of maximum likelihood, and the method of empirical characteristic function. A real data application is presented. Finally, extensions to the multivariate case are outlined.

KEYWORDS:

• Estimation
• Generalized normal distribution
• Weighting function.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E99

Acknowledgments

The authors would like to thank the two referees for careful reading and comments which greatly improved the article.