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

@article{Goerg2009LambertWR, title={Lambert W random variables—a new family of generalized skewed distributions with applications to risk estimation}, author={Georg M. Goerg}, journal={The Annals of Applied Statistics}, year={2009}, volume={5}, pages={2197-2230} }

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… Expand

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