An opposite Gaussian product inequality

Oliver Russell and Wei Sun

Statistics & Probability Letters, 2022, vol. 191, issue C

Abstract: The long-standing Gaussian product inequality (GPI) conjecture states that E[∏j=1n|Xj|αj]≥∏j=1nE[|Xj|αj] for any centered Gaussian random vector (X1,…,Xn) and any non-negative real numbers αj, j=1,…,n. In this note, we prove a novel “opposite GPI” for centered bivariate Gaussian random variables when −1<α1<0 and α2>0: E[|X1|α1|X2|α2]≤E[|X1|α1]E[|X2|α2]. This completes the picture of bivariate Gaussian product relations.

Keywords: Bivariate Gaussian random variables; Gaussian product inequality conjecture; Opposite Gaussian product inequality; Hypergeometric function (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2022.109656

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