Test of Normality Against Generalized Exponential Power Alternatives

Abstract

The family of symmetric generalized exponential power (GEP) densities offers a wide range of tail behaviors, which may be exponential, polynomial, and/or logarithmic. In this article, a test of normality based on Rao's score statistic and this family of GEP alternatives is proposed. This test is tailored to detect departures from normality in the tails of the distribution. The main interest of this approach is that it provides a test with a large family of symmetric alternatives having non-normal tails. In addition, the test's statistic consists of a combination of three quantities that can be interpreted as new measures of tail thickness. In a Monte-Carlo simulation study, the proposed test is shown to perform well in terms of power when compared to its competitors.

Keywords:

• Generalized exponential power
• Rao's score test
• Symmetric distributions
• Tail behavior
• Test of normality

Mathematics Subject Classification:

• 62E20
• 62E25
• 62F03
• 60F05

Acknowledgments

This research of A. Desgagné, P. Lafaye de Micheaux, and A. Leblanc was supported by the Natural Sciences and Engineering Research Council of Canada. The authors are also grateful for the good time spent together during their doctoral years, when this project started following discussions at a student seminar in the Département de Mathématiques et de Statistique of the Université de Montréal.