An alternative skew exponential power distribution formulation

• Published in: Communications in statistics. Theory and methods Vol. 48; no. 12; pp. 3005 - 3024
• Main Author: Hutson, Alan D.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 18-06-2019; Taylor & Francis Ltd
• Subjects: beta normal distribution; Economic models; Electric power distribution; expectiles; Kurtosis; Mathematical models; Maximum likelihood estimation; Normal distribution; Parameters; quantiles; skew Laplace distribution; Skew normal distribution; Skewed distributions; expectiles; quantiles; beta normal distribution; skew Laplace distribution; skew normal distribution
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2018.1473600

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.