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，已有多种分布及分布族被提出，例如偏正态分布及其相关分布。Lambert W随机变量提供了一种替代方法，该方法并非构建新分布，而是提出某种变换（Goerg, 2011）。这种变换允许从任意分布构造出Lambert W偏斜版本。我们选择Lambert W正态分布作为自然起点，并因指数分布形式简单且形状特征易于在偏斜后产生适用于损失模型的较厚尾部，也纳入Lambert W指数分布。在理论部分，我们重点研究所得分布的数学性质，包括偏斜度的取值范围。在实践部分，基于真实保险数据评估了相应Lambert W变换分布的适用性，并将结果与使用常见损失分布所得结果进行了比较。