Lambert W random variables—a new family of generalized skewed distributions with applications to risk estimation
By Georg M. Goerg. 2009
82 citations recorded by the source corpus.
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 this http URL developed by the author is publicly available (this http URL).
Subfields: Biomedical Engineering, Statistical and Nonlinear Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/75a9e0234abcffcac01c8c8ee1ff13499b160c06
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In Biomedical Engineering
In Statistical and Nonlinear Physics
In Statistics and Probability
Citations in the corpus
- Finding Optimal Normalizing Transformations via bestNormalize (2021, methodology): “The Lambert W x F transformation, proposed in Goerg (2011) and implemented in the LambertW package, is essentially a mechanism that de-skews a random variable X using moments.”
- Ordered quantile normalization: a semiparametric transformation built for the cross-validation era (2019, methodology): “The Lambert WxF ‘Gaussianizing’ transformation is a similar approach that uses maximum likelihood to estimate a parametric function that best normalizes a skewed or a heavy-tailed distribution [7].”