论文标题
一个有用的脂肪分配家庭
A useful family of fat-tailed distributions
论文作者
论文摘要
有人认为，有必要在极端的尾巴中变薄的脂肪分布。引入了3参数分布，该分布在视觉上类似于T-分布和插入正态分布和Cauchy分布之间的插值。它是胖尾，但具有所有时刻有限的，并且存在瞬间的功能。对于敏感性分析，它将作为替代t分布的替代方法，以检查结果的鲁棒性或需要有限矩的计算（例如在期权定价中）。它可以至少以两种方式进行概率激励，要么是长尾分布的随机变薄，也可以作为正态分布方差的随机变化。描述了其属性，提供了随机数生成的算法，并提供了其在数据拟合中使用的示例。还讨论了一些相关的分布，包括不对称和多元分布。
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and the Cauchy distribution. It is fat-tailed, but has all moments finite, and the moment-generating function exists. It would be useful as an alternative to the t-distribution for a sensitivity analysis to check the robustness of results or for computations where finite moments are needed, such as in option-pricing. It can be motivated probabilistically in at least two ways, either as the random thinning of a long-tailed distribution, or as random variation of the variance of a normal distribution. Its properties are described, algorithms for random-number generation are provided, and examples of its use in data-fitting given. Some related distributions are also discussed, including asymmetric and multivariate distributions.
