  Several distributions and families of distributions are proposed to model
skewed data, think, e.g., of skew-normal and related distributions. Lambert W
random variables offer an alternative approach where, instead of constructing a
new distribution, a certain transform is proposed (Goerg, 2011). Such an
approach allows the construction of a Lambert W skewed version from any
distribution. We choose Lambert W normal distribution as a natural starting
point and also include Lambert W exponential distribution due to the simplicity
and shape of the exponential distribution, which, after skewing, may produce a
reasonably heavy tail for loss models. In the theoretical part, we focus on the
mathematical properties of obtained distributions, including the range of
skewness. In the practical part, the suitability of corresponding Lambert W
transformed distributions is evaluated on real insurance data. The results are
compared with those obtained using common loss distributions.
