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A characterization of normality via convex likelihood ratios

Abstract

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

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