A Note on the Kurtosis Ordering of the Generalized Secant Hyperbolic Distribution

Journal article
(Original article)


Publication Details

Author(s): Klein I, Fischer M
Journal: Communications in Statistics-Theory and Methods
Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis
Publication year: 2008
Volume: 37
Journal issue: 1
Pages range: 1-7
ISSN: 0361-0926
Language: English


Abstract


Two major generalizations of the hyperbolic secant distribution have been proposed in the statistical literature which both introduce an additional parameter that governs the kurtosis of the generalized distribution. The generalized hyperbolic secant (GHS) distribution was introduced by Harkness and Harkness (1968) who considered the pth convolution of a hyperbolic secant distribution. Another generalization, the so-called generalized secant hyperbolic (GSH) distribution, was recently suggested by Vaughan (2002). In contrast to the GHS distribution, the cumulative and inverse cumulative distribution function of the GSH distribution are available in closed-form expressions. We use this property to prove that the additional shape parameter of the GSH distribution is actually a kurtosis parameter in the sense of van Zwet (1964).


FAU Authors / FAU Editors

Fischer, Matthias Prof. Dr.
Fachbereich Wirtschaftswissenschaften
Klein, Ingo Prof. Dr.
Lehrstuhl für Statistik und Ökonometrie


How to cite

APA:
Klein, I., & Fischer, M. (2008). A Note on the Kurtosis Ordering of the Generalized Secant Hyperbolic Distribution. Communications in Statistics-Theory and Methods, 37(1), 1-7. https://dx.doi.org/10.1080/03610920701648839

MLA:
Klein, Ingo, and Matthias Fischer. "A Note on the Kurtosis Ordering of the Generalized Secant Hyperbolic Distribution." Communications in Statistics-Theory and Methods 37.1 (2008): 1-7.

BibTeX: 

Last updated on 2018-28-08 at 14:23