Academic Journal
A combinatorial proof of the Gaussian product inequality beyond the MTP2 case
| العنوان: | A combinatorial proof of the Gaussian product inequality beyond the MTP2 case |
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| المؤلفون: | Genest Christian, Ouimet Frédéric |
| المصدر: | Dependence Modeling, Vol 10, Iss 1, Pp 236-244 (2022) |
| بيانات النشر: | De Gruyter, 2022. |
| سنة النشر: | 2022 |
| المجموعة: | LCC:Science (General) LCC:Mathematics |
| مصطلحات موضوعية: | complete monotonicity, gamma function, gaussian product inequality, gaussian random vector, moment inequality, multinomial, multivariate normal, polygamma function, primary 60e15, secondary 05a20, 33b15, 62e15, 62h10, 62h12, Science (General), Q1-390, Mathematics, QA1-939 |
| الوصف: | A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that each component of a centered Gaussian random vector X=(X1,…,Xd){\boldsymbol{X}}=\left({X}_{1},\ldots ,{X}_{d}) of arbitrary length can be written as a linear combination, with coefficients of identical sign, of the components of a standard Gaussian random vector. This condition on X{\boldsymbol{X}} is shown to be strictly weaker than the assumption that the density of the random vector (∣X1∣,…,∣Xd∣)\left(| {X}_{1}| ,\ldots ,| {X}_{d}| ) is multivariate totally positive of order 2, abbreviated MTP2{\text{MTP}}_{2}, for which the GPI is already known to hold. Under this condition, the paper highlights a new link between the GPI and the monotonicity of a certain ratio of gamma functions. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 2300-2298 |
| Relation: | https://doaj.org/toc/2300-2298 |
| DOI: | 10.1515/demo-2022-0116 |
| URL الوصول: | https://doaj.org/article/7c9b1e90d6614bba8722b644ace788d4 |
| رقم الانضمام: | edsdoj.7c9b1e90d6614bba8722b644ace788d4 |
| قاعدة البيانات: | Directory of Open Access Journals |
Full Text Finder | تدمد: | 23002298 |
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| DOI: | 10.1515/demo-2022-0116 |