An alternative skew exponential power distribution formulation

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.

Keywords:

• Skew normal distribution
• skew Laplace distribution
• beta normal distribution
• quantiles
• expectiles

Acknowledgements

We wish to thank the three referees whose thoughtful reviews vastly improved this paper.

Additional information

Funding

This work was supported by Roswell Park Cancer Institute and National Cancer Institute (NCI) grant P30CA016056, National Science Foundation IIS-1514204 and NRG Oncology Statistical and Data Management Center grant U10CA180822.