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A characterization of the normal distribution by the independence of a pair of random vectors

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  • Ejsmont, Wiktor

Abstract

Kagan and Shalaevski (1967) have shown that if the random variables X1,…,Xn are i.i.d. and the distribution of ∑i=1n(Xi+ai)2ai∈R depends only on ∑i=1nai2, then each Xi∼N(0,σ). In this paper, we will give other characterizations of the normal distribution which are formulated in a similar spirit.

Suggested Citation

  • Ejsmont, Wiktor, 2016. "A characterization of the normal distribution by the independence of a pair of random vectors," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 1-5.
  • Handle: RePEc:eee:stapro:v:114:y:2016:i:c:p:1-5
    DOI: 10.1016/j.spl.2016.02.011
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    References listed on IDEAS

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    1. Cook, Lyle, 1971. "A characterization of the normal distribution by the independence of a pair of random vectors and a property of the noncentral chi-square statistic," Journal of Multivariate Analysis, Elsevier, vol. 1(4), pages 457-460, December.
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    Cited by:

    1. Jacobovic, Royi & Kella, Offer, 2022. "A characterization of normality via convex likelihood ratios," Statistics & Probability Letters, Elsevier, vol. 186(C).

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