Modeling Skewness and Kurtosis with the S-EGSH

• Activity Number: 457
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): David C. Vaughan*+
• Companies: Wilfrid Laurier University
• Keywords: Skewness ; Kurtosis ; S-EGSH ; Unimodal

Abstract

The fundamental Skew-Extended Generalized Secant Hyperbolic (S-EGSH) distributions, introduced by Vaughan (JSM 2007) and further generalized in this work, provide a rich family in which to model both skewness and kurtosis. Basic properties of the symmetric Generalized Secant Hyperbolic (GSH) include: unimodality; all moments are finite; and any kurtosis for regular unimodal distributions can be modeled within the GSH family. These properties make the GSH family a natural one to extend to include skewness through the introduction of shape parameters, and the S-EGSH family remains relatively simple and tractable. In this talk, we consider the range of combinations of skewness and kurtosis that can be represented through examination of moment ratio diagrams (Craig 1936) and other measures and plots associated with the S-eGSH.