Sinh-arcsinh distributions
Sinh-arcsinh distributions
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DOI：
10.1093/biomet/asp053
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发表时间：
2009-12-01
期刊：
影响因子：
2.7
通讯作者：
Pewsey, Arthur
中科院分区：
文献类型：
--
作者：
Jones, M. C.;Pewsey, Arthur
我们引入了Sinh-arcsinh变换，并由此将它应用于一个除了位置和尺度以外没有其他参数的生成分布，通常是正态分布，这是一族新的Sinh-arcsinh分布。该四参数族具有对称和倾斜的成员，并允许尾重比生成分布的尾重更重和更轻。正态分布在这个家族中的中心位置提供了正态分布的似然比检验，这些检验优于正态检验中的最先进水平，因为它们针对的替代方案的范围非常强大。对称性的似然比检验也是可用的，而且非常成功。全族的三参数对称和不对称子族也很有趣。重尾对称正弦分布表现得像约翰逊S-U分布，而它们的轻尾分布表现得像正态分布，正态分布允许两者之间的无缝过渡，通过正态分布，由单个参数控制。Sinh-arcsinh家族非常容易处理，并探索了许多性质。进行了似然推断，包括一种有吸引力的再参数化法。文中给出了应用实例。考虑了一个多变量版本。讨论了选项和扩展。
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 S-U 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.