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

Department of Statistics

The Hebrew University of Jerusalem

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

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

Keywords

Characterization of probability distributions
Convex likelihood ratio
Gaussian
Multivariate normal

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2022.109455

Cite this

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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).",

keywords = "Characterization of probability distributions, Convex likelihood ratio, Gaussian, Multivariate normal",

author = "Royi Jacobovic and Offer Kella",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

month = jul,

doi = "10.1016/j.spl.2022.109455",

language = "الإنجليزيّة",

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T1 - A characterization of normality via convex likelihood ratios

AU - Jacobovic, Royi

AU - Kella, Offer

PY - 2022/7

Y1 - 2022/7

N2 - 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).

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

KW - Gaussian

KW - Multivariate normal

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U2 - 10.1016/j.spl.2022.109455

DO - 10.1016/j.spl.2022.109455

M3 - مقالة

SN - 0167-7152

VL - 186

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 109455

ER -

A characterization of normality via convex likelihood ratios

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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