Sinh-arcsinh distributions

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