The Skew Generalized Secant Hyperbolic Extension (SGSHE): An Introduction

• Activity Number: 698
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): David Vaughan*+
• Companies: Wilfrid Laurier Univ
• Keywords: generalized secant hyperbokic ; skewness ; entropy

Abstract

There are many examples of financial data sets that exhibit either non-normal kurtosis, asymmetry or both. As well, non-normality arises in other scientific investigations, such as gene expression (Hardin and Wilson (2009)) and chemical and nuclear measurements (Currie (2001)). A number of methods of creating skew families, typically starting with a symmetric distribution and introducing a skewing mechanism, have been proposed. In this talk, a simple extension of the (symmetric) generalized secant hyperbolic distributions introduced in Vaughan (2002) that incorporates skewness while retaining excellent analytic properties is introduced. These are unimodal distributions, with all moments finite. Any value of the Arnold-Groeneveld (1995) coefficient of skewness can be obtained, in combination with a wide range of kurtosis. The distributions are explicit and, as location-scale models, can be analyzed by maximum likelihood. Quantities such as the cdf, mgf, and measures of entropy are discussed.