A combinatorial proof of the Gaussian product inequality beyond the \(\mathrm{MTP}_2\) case

DOI10.1515/demo-2022-0116zbMath1497.60022arXiv2112.12283OpenAlexW4293010920MaRDI QIDQ2172584

Christian Genest, Frédéric Ouimet

Publication date: 16 September 2022

Published in: Dependence Modeling (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.12283

zbMATH Keywords

gamma functionmultivariate normalpolygamma functionGaussian random vectormultinomialcomplete monotonicitymoment inequalityGaussian product inequality

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Estimation in multivariate analysis (62H12) Inequalities; stochastic orderings (60E15) Exact distribution theory in statistics (62E15) Gamma, beta and polygamma functions (33B15) Combinatorial inequalities (05A20)

Related Items (5)

Some new Gaussian product inequalities ⋮ A short proof of a strong form of the three dimensional Gaussian product inequality ⋮ Quantitative versions of the two-dimensional Gaussian product inequalities ⋮ Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality ⋮ Miscellaneous results related to the Gaussian product inequality conjecture for the joint distribution of traces of Wishart matrices

Uses Software

• MathOverflow

Cites Work

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