多元偏正态-Tukey-h分布
A Multivariate Skew-Normal-Tukey-h Distribution
AI总结：
本文提出多元偏正态-Tukey-h分布，通过Tukey-h变换扩展偏正态分布以处理重尾数据，在边际峰度差异显著时优于偏t分布，并给出线性计算复杂度的参数估计方法及模拟与实例应用。
摘要：
我们通过将服从偏正态分布的随机向量进行逐分量的Tukey-h变换，引入了一族新的多元分布。所提出的分布被称为偏正态-Tukey-h分布，是偏正态分布的一种扩展，用于处理重尾数据。我们将该分布与偏t分布进行比较，偏t分布是偏正态分布的另一种用于建模尾部厚度的扩展，并证明当边际峰度存在显著差异时，所提出的分布更为合适。此外，我们推导了该分布许多吸引人的随机性质，并提供了一种参数估计方法，其计算需求随维度线性增加。通过模拟以及葡萄酒和风速数据的应用，我们展示了如何基于多元偏正态-Tukey-h分布进行推断。
英文摘要：
We introduce a new family of multivariate distributions by taking the component-wise Tukey-h transformation of a random vector following a skew-normal distribution. The proposed distribution is named the skew-normal-Tukey-h distribution and is an extension of the skew-normal distribution for handling heavy-tailed data. We compare this proposed distribution to the skew-t distribution, which is another extension of the skew-normal distribution for modeling tail-thickness, and demonstrate that when there are substantial differences in marginal kurtosis, the proposed distribution is more appropriate. Moreover, we derive many appealing stochastic properties of the proposed distribution and provide a methodology for the estimation of the parameters in which the computational requirement increases linearly with the dimension. Using simulations, as well as a wine and a wind speed data application, we illustrate how to draw inferences based on the multivariate skew-normal-Tukey-h distribution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
