关于折叠和双截尾多元广义斜正态分布的矩
On moments of folded and doubly truncated multivariate extended skew-normal distributions
摘要：
本文建立了多元扩展偏态分布（ESN）密度函数积分的递推关系，包括Azzalini和Dalla-Valle（1996）提出的偏态分布（SN）和流行的多元正态分布。这些递归提供了一个快速计算任意阶的产品的时刻的多元截断扩展的偏态正态分布和多元折叠扩展的偏态正态分布与产品的时刻作为副产品。除了递归方法，我们认识到，任何任意时刻的截断多元扩展的偏态分布可以计算使用相应的时刻截断多元正态分布，指出了一种更快的算法，因为它的计算所需的积分数较少，结果更简单的评估。由于有几种方法可用于计算多元截断正态分布的前两个时刻，我们提出了一种优化的方法，提供了更好的性能，在时间和精度方面，除了考虑极端情况下，其他方法失败。R MomTrunc包为从业者提供了这些新的有效方法。
英文摘要：
This paper develops recurrence relations for integrals that relate the density of multivariate extended skew-normal (ESN) distribution, including the well-known skew-normal (SN) distribution introduced by Azzalini and Dalla-Valle (1996) and the popular multivariate normal distribution. These recursions offer a fast computation of arbitrary order product moments of the multivariate truncated extended skew-normal and multivariate folded extended skew-normal distributions with the product moments as a byproduct. In addition to the recurrence approach, we realized that any arbitrary moment of the truncated multivariate extended skew-normal distribution can be computed using a corresponding moment of a truncated multivariate normal distribution, pointing the way to a faster algorithm since a less number of integrals is required for its computation which result much simpler to evaluate. Since there are several methods available to calculate the first two moments of a multivariate truncated normal distribution, we propose an optimized method that offers a better performance in terms of time and accuracy, in addition to consider extreme cases in which other methods fail. The R MomTrunc package provides these new efficient methods for practitioners.
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