Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions

Raúl Alejandro Morán-Vásquez (), Edwin Zarrazola and Daya K. Nagar
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Raúl Alejandro Morán-Vásquez: Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, Colombia
Edwin Zarrazola: Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, Colombia
Daya K. Nagar: Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, Colombia

Mathematics, 2023, vol. 11, issue 16, 1-16

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.

Keywords: marginal distribution; Monte Carlo integration; multivariate skew-normal/independent distributions; random vector; truncated distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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