Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality
نویسندگان
چکیده
We prove the three-dimensional Gaussian product inequality (GPI)E[X12X22m2X32m3]≥E[X12]E[X22m2]E[X32m3] for any centered random vector (X1,X2,X3) and m2,m3∈N. discover a novel moment ratio |E[X22m2+1X32m3+1]|E[X22m2X32m3], which implies 3D-GPI. The interplay between computing hard analysis plays crucial role in proofs.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2023
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2023.127410