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Sinh-arcsinh distributions

Jones, M. C. and Pewsey, Arthur (2009). Sinh-arcsinh distributions. Biometrika, 96(4) pp. 761–780.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1093/biomet/asp053
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Abstract

We introduce the sinh-arcsinh transformation and hence, by applying it to a generating distribution with no parameters other than location and scale, usually the normal, a new family of sinh-arcsinh distributions. This four-parameter family has symmetric and skewed members and allows for tailweights that are both heavier and lighter than those of the generating distribution. The central place of the normal distribution in this family affords likelihood ratio tests of normality that are superior to the state-of-the-art in normality testing because of the range of alternatives against which they are very powerful. Likelihood ratio tests of symmetry are also available and are very successful. Three-parameter symmetric and asymmetric subfamilies of the full family are also of interest. Heavy-tailed symmetric sinh-arcsinh distributions behave like Johnson SU distributions, while their light-tailed counterparts behave like sinh-normal distributions, the sinh-arcsinh family allowing a seamless transition between the two, via the normal, controlled by a single parameter. The sinh-arcsinh family is very tractable and many properties are explored. Likelihood inference is pursued, including an attractive reparameterization. Illustrative examples are given. A multivariate version is considered. Options and extensions are discussed.

Item Type: Journal Article
Copyright Holders: 2009 Biometrika Trust
ISSN: 1464-3510
Extra Information: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version is available online at http://biomet.oxfordjournals.org/.
Keywords: heavy tail; Johnson's SU distribution; light tail; sinh-normal distribution; skew-normal distribution; skewness; transformation
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22510
Depositing User: Sarah Frain
Date Deposited: 10 Aug 2010 11:39
Last Modified: 30 Nov 2012 12:39
URI: http://oro.open.ac.uk/id/eprint/22510
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