A characterization of normality via convex likelihood ratios

Royi Jacobovic; Offer Kella

doi:10.1016/j.spl.2022.109455

A characterization of normality via convex likelihood ratios

Royi Jacobovic, Offer Kella^*

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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).

Original language	English
Article number	109455
Journal	Statistics and Probability Letters
Volume	186
DOIs	https://doi.org/10.1016/j.spl.2022.109455
State	Published - Jul 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier B.V.

Keywords

Characterization of probability distributions
Convex likelihood ratio
Gaussian
Multivariate normal

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10.1016/j.spl.2022.109455

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title = "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 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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author = "Royi Jacobovic and Offer Kella",

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AB - 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).

KW - Characterization of probability distributions

KW - Convex likelihood ratio

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VL - 186

JO - Statistics and Probability Letters

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A characterization of normality via convex likelihood ratios

Abstract

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Keywords

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