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arXiv · 2110.14173

A characterization of normality via convex likelihood ratios

Royi Jacobovic·Offer Kella
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Abstract

This work includes a new characterization of the multivariate normal distribution. In particular, it is shown that a positive density function $f$ is Gaussian if and only if the $f(x+ y)/f(x)$ is convex in $x$ for every $y$. This result has implications to recent research regarding inadmissibility of a test studied by Moran~(1973).

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Royi Jacobovic, Offer Kella. 2022-03-03. A characterization of normality via convex likelihood ratios. https://arxiv.org/abs/2110.14173

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