A characterization of normality via convex likelihood ratios

10/27/2021

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by   Royi Jacobovic, et al.

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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).