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

Wiktor Ejsmont

Statistics & Probability Letters, 2016, vol. 114, issue C, 1-5

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.

Keywords: Cumulants; Characterization of normal distribution (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2016.02.011

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