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 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.

• Autores: Morán Vásquez, Raúl Alejandro; Zarrazola, Edwin; Nagar, Daya K.
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2023
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/46089
• Acceso en línea: https://hdl.handle.net/10495/46089
• Palabra clave: Marginal distributions; Mathematics; Statistics; Marginal distribution; Monte Carlo integration; Multivariate Skew-normal; Independent distributions; Random vector; Truncated distribution
• Rights: openAccess
• License: http://purl.org/coar/access_right/c_abf2