On a characterization of the normal distribution by means of identically distributed linear forms

M. Riedel

Journal of Multivariate Analysis, 1985, vol. 16, issue 2, 241-252

Abstract: Let X1, X2,..., be independent, identically distributed random variables. Suppose that the linear forms L1 = [Sigma]j=1[infinity]ajXj and L2 = [Sigma]j=1[infinity]bjXj exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X1 is normally distributed are presented. The result is an extension of a theorem of [4], 207-243, 247-290) concerning the case that the linear forms L1 and L2 have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions.

Keywords: Characterization; linear; forms; meromorphic; functions; normal; distribution (search for similar items in EconPapers)
Date: 1985
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