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A characterization of distributions of independent random vectors by the independence of transformed vectors

Authors:	Lyle Cook

Affiliation:	Department of Mathematics and Statistics, Oklahoma State University, Stillwater, Oklahoma 74074 USA

Abstract:	If W and Z are independent random vectors and Y₁, Y₂, …, Y_n are the result of a transformation satisfying certain general conditions then W and Z are distributed according to a certain class of densities if and only if for suitable q, (Y₁, …, Y_q) and (Y_q+1, …, Y_n) are independent.

Keywords:	62H05 Characterization normal distribution gamma distribution Cauchy equation
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