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- Title
Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions.
- Authors
Morán-Vásquez, Raúl Alejandro; Zarrazola, Edwin; Nagar, Daya K.
- Abstract
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.
- Subjects
PROBABILITY density function; RANDOM variables; SKEWNESS (Probability theory); AFFINE transformations; MARGINAL distributions; PROBABILITY theory
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 16, p3579
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11163579