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Originating from a system theory and an input/output point of view, Iintroduce a new class of generalized distributions. A parametric nonlineartransformation converts a random variable $X$ into a so-called Lambert $W$random variable $Y$, which allows a very flexible approach to model skeweddata. Its shape depends on the shape of $X$ and a skewness parameter $\gamma$.In particular, for symmetric $X$ and nonzero $\gamma$ the output $Y$ is skewed.Its distribution and density function are particular variants of their inputcounterparts. Maximum likelihood and method of moments estimators arepresented, and simulations show that in the symmetric case additionalestimation of $\gamma$ does not affect the quality of other parameterestimates. Applications in finance and biomedicine show the relevance of thisclass of distributions, which is particularly useful for slightly skewed data.A practical by-result of the Lambert $W$ framework: data can be "unskewed." The$R$ package http://cran.r-project.org/web/packages/LambertWLambertW developedby the author is publicly available (http://cran.r-project.orgCRAN).

Lambert W random variables - a new family of generalized skewed distributions with applications to risk estimation