We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to potentially heavier-tailed distributions. Sub-Weibull distributions are parameterized by a positive tail index $\theta$ and reduce to sub-Gaussian distributions for $\theta=1/2$ and to sub-Exponential distributions for $\theta=1$. A characterisation of the sub-Weibull property based on moments and on the moment generating function is provided and properties of the class are studied. An estimation procedure for the tail parameter is proposed and is applied to an example stemming from Bayesian deep learning.

翻译：我们提出次Weibull分布的概念,其特征为比Weibull分布的尾巴轻的尾巴(或与Weibull分布的右尾巴一样轻),这个新颖的分类将亚Gausian和亚Explicate家族概括为潜在更重的分布。亚Weibull分布的参数为正尾指数$\theta$,并减少至亚Gausian分布,以$\theta=1/2美元为单位,以及以美元=1美元为单位的亚特惠分布。提供了基于时空生成功能的亚Weibull属性的特性,并研究了该类特性。提出了尾参数的估计程序,并用于贝叶斯人深思学习的一个例子。