Open Access
June 2005 The effect of non-normality on the distribution of sample fourth order cumulant under elliptical populations
Yosihito Maruyama
Author Affiliations +
SUT J. Math. 41(2): 97-116 (June 2005). DOI: 10.55937/sut/1159986270

Abstract

In this paper, we consider the effect of non-normality on the distribution of the sample fourth order cumulant in elliptical distributions. Asymptotic properties of the distribution of the sample fourth order cumulant is presented under non-normality, especially, the class of elliptical populations in detail. Asymptotic expansion formulas for the distributions are derived by a perturbation method. Finally, the numerical results are obtained.

Acknowledgments

The author would like to express his sincere gratitude to Professor Takashi Seo for his kind guidance and constant encouragement. The author also thanks the referee for the comments that were useful very much for the revision of the paper.

Citation

Download Citation

Yosihito Maruyama. "The effect of non-normality on the distribution of sample fourth order cumulant under elliptical populations." SUT J. Math. 41 (2) 97 - 116, June 2005. https://doi.org/10.55937/sut/1159986270

Information

Received: 11 April 2005; Revised: 23 July 2005; Published: June 2005
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1159986270

Subjects:
Primary: 62E20 , 62F12 , 62H10

Keywords: asymptotic expansion , bias correction , cumulant , elliptical distribution , kurtosis parameter , moment parameter , non-normality

Rights: Copyright © 2005 Tokyo University of Science

Vol.41 • No. 2 • June 2005
Back to Top