A characterization of normality via convex likelihood ratios

Published 27 Oct 2021 in math.ST, math.PR, and stat.TH | (2110.14173v2)

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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