تقرير
On Elliptical and Inverse Elliptical Wishart distributions: Review, new results, and applications
| العنوان: | On Elliptical and Inverse Elliptical Wishart distributions: Review, new results, and applications |
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| المؤلفون: | Ayadi, Imen, Bouchard, Florent, Pascal, Frédéric |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Statistics - Methodology |
| الوصف: | This paper deals with matrix-variate distributions, from Wishart to Inverse Elliptical Wishart distributions over the set of symmetric definite positive matrices. Similar to the multivariate scenario, (Inverse) Elliptical Wishart distributions form a vast and general family of distributions, encompassing, for instance, Wishart or $t$-Wishart ones. The first objective of this study is to present a unified overview of Wishart, Inverse Wishart, Elliptical Wishart, and Inverse Elliptical Wishart distributions through their fundamental properties. This involves leveraging the stochastic representation of these distributions to establish key statistical properties of the Normalized Wishart distribution. Subsequently, this enables the computation of expectations, variances, and Kronecker moments for Elliptical Wishart and Inverse Elliptical Wishart distributions. As an illustrative application, the practical utility of these generalized Elliptical Wishart distributions is demonstrated using a real electroencephalographic dataset. This showcases their effectiveness in accurately modeling heterogeneous data. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.17468 |
| رقم الأكسشن: | edsarx.2404.17468 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |