On moments of folded and doubly truncated multivariate extended skew-normal distributions
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Publication:6350064
DOI10.1080/10618600.2021.2000869arXiv2009.13488MaRDI QIDQ6350064
Christian E. Galarza Morales, Larissa A. Matos, Victor H. Lachos, Dipak K. Dey
Publication date: 28 September 2020
Abstract: 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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