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.

翻译：为对偏斜数据进行建模，研究者提出了若干分布及分布族，例如偏正态分布及相关分布。Lambert W随机变量提供了另一种方法：相比于构建新分布，该方法提出了某种变换（Goerg, 2011）。此类方法允许从任意分布出发构造Lambert W偏斜版本。我们选择Lambert W正态分布作为自然起点，同时因指数分布形式简单且形状特性适宜，也纳入Lambert W指数分布——在偏斜后，该分布可为损失模型产生相当厚重的尾部。在理论部分，我们重点研究所得分布的数学性质，包括偏斜度范围。在实践部分，对应Lambert W变换分布的适用性通过真实保险数据进行评估，并将结果与常用损失分布的结果进行比较。