  Originating from a system theory and an input/output point of view, I
introduce a new class of generalized distributions. A parametric nonlinear
transformation converts a random variable $X$ into a so-called Lambert $W$
random variable $Y$, which allows a very flexible approach to model skewed
data. 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 input
counterparts. Maximum likelihood and method of moments estimators are
presented, and simulations show that in the symmetric case additional
estimation of $\gamma$ does not affect the quality of other parameter
estimates. Applications in finance and biomedicine show the relevance of this
class 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 developed
by the author is publicly available (http://cran.r-project.orgCRAN).
