An alternative skew exponential power distribution formulation. Issue 12 (18th June 2019)

• Record Type: Journal Article
• Authors: Hutson, Alan D.
• Is Part Of: Communications in statistics. Volume 48:Issue 12(2019)
• Page Start: 3005
• Page End: 3024
• Publication Date: 2019-06-18
• Subjects: Skew normal distribution -- skew Laplace distribution -- beta normal distribution -- quantiles -- expectiles; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1473600
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this note we propose a newly formulated skew exponential power distribution that behaves substantially better than previously defined versions. This new model performs very well in terms of the large sample behavior of the maximum likelihood estimation procedure when compared to the classically defined four parameter model defined by Azzalini. More recently, approaches to defining a skew exponential power distribution have used five or more parameters. Our approach improves upon previous attempts to extend the symmetric power exponential family to include skew alternatives by maintaining a minimum set of four parameters corresponding directly to location, scale, skewness and kurtosis. We illustrate the utility of our proposed model using translational and clinical data sets.