A characterization of the normal distribution by the independence of a pair of random vectors and a property of the noncentral chi-square statistic

Lyle Cook

Journal of Multivariate Analysis, 1971, vol. 1, issue 4, 457-460

Abstract: It is known that if the statistic Y = [Sigma]j=1n(Xj + aj)2 is drawn from a population which is distributed N(0, [sigma]) then the distribution of Y depends on only. Kagan and Shalaevski [2] have shown that if the random variables X1, X2, ..., Xn are independent and identically distributed and the distribution of Y depends only on , then each Xj is distributed N(0, [sigma]). It is shown below that if the random vectors (X1, ..., Xm) and (Xm+1, ..., Xn) are independent and the distribution of Y depends only on , then all Xj are independent and distributed N(0, [sigma]).

Keywords: Characterization; normal; distribution; chi-square; statistic; Cauchy; equation; integral; transform (search for similar items in EconPapers)
Date: 1971
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Citations: View citations in EconPapers (1)

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