Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions
In this article, we derive a closed-form expression for computing the probabilities of p-dimensional rectangles by means of a multivariate skew-normal distribution. We use a stochastic representation of the multivariate skew-normal/independent distributions to derive expressions that relate their pr...
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Published in | Mathematics (Basel) Vol. 11; no. 16; p. 3579 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Basel
MDPI AG
01.08.2023
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Subjects | |
Online Access | Get full text |
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Summary: | In this article, we derive a closed-form expression for computing the probabilities of p-dimensional rectangles by means of a multivariate skew-normal distribution. We use a stochastic representation of the multivariate skew-normal/independent distributions to derive expressions that relate their probability density functions to the expected values of positive random variables. We also obtain an analogous expression for probabilities of p-dimensional rectangles for these distributions. Based on this, we propose a procedure based on Monte Carlo integration to evaluate the probabilities of p-dimensional rectangles through multivariate skew-normal/independent distributions. We use these findings to evaluate the probability density functions of a truncated version of this class of distributions, for which we also suggest a scheme to generate random vectors by using a stochastic representation involving a truncated multivariate skew-normal random vector. Finally, we derive distributional properties involving affine transformations and marginalization. We illustrate graphically several of our methodologies and results derived in this article. |
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ISSN: | 2227-7390 2227-7390 |
DOI: | 10.3390/math11163579 |