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 <i>p</i>-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 t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3579 |
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| author | Raúl Alejandro Morán-Vásquez Edwin Zarrazola Daya K. Nagar |
| author_facet | Raúl Alejandro Morán-Vásquez Edwin Zarrazola Daya K. Nagar |
| author_sort | Raúl Alejandro Morán-Vásquez |
| collection | DOAJ |
| description | In this article, we derive a closed-form expression for computing the probabilities of <i>p</i>-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 <i>p</i>-dimensional rectangles for these distributions. Based on this, we propose a procedure based on Monte Carlo integration to evaluate the probabilities of <i>p</i>-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. |
| first_indexed | 2024-03-10T23:45:35Z |
| format | Article |
| id | doaj.art-6a109daa52234a1c90cd5fb86888f98b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:45:35Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6a109daa52234a1c90cd5fb86888f98b2023-11-19T02:04:05ZengMDPI AGMathematics2227-73902023-08-011116357910.3390/math11163579Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent DistributionsRaúl Alejandro Morán-Vásquez0Edwin Zarrazola1Daya K. Nagar2Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, ColombiaInstituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, ColombiaInstituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, ColombiaIn this article, we derive a closed-form expression for computing the probabilities of <i>p</i>-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 <i>p</i>-dimensional rectangles for these distributions. Based on this, we propose a procedure based on Monte Carlo integration to evaluate the probabilities of <i>p</i>-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.https://www.mdpi.com/2227-7390/11/16/3579marginal distributionMonte Carlo integrationmultivariate skew-normal/independent distributionsrandom vectortruncated distribution |
| spellingShingle | Raúl Alejandro Morán-Vásquez Edwin Zarrazola Daya K. Nagar Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions Mathematics marginal distribution Monte Carlo integration multivariate skew-normal/independent distributions random vector truncated distribution |
| title | Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions |
| title_full | Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions |
| title_fullStr | Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions |
| title_full_unstemmed | Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions |
| title_short | Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions |
| title_sort | some theoretical and computational aspects of the truncated multivariate skew normal independent distributions |
| topic | marginal distribution Monte Carlo integration multivariate skew-normal/independent distributions random vector truncated distribution |
| url | https://www.mdpi.com/2227-7390/11/16/3579 |
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