A characterization of normality via convex likelihood ratios

Royi Jacobovic and Offer Kella

Statistics & Probability Letters, 2022, vol. 186, issue C

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).

Keywords: Characterization of probability distributions; Multivariate normal; Gaussian; Convex likelihood ratio (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109455

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