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Constraints on distributions imposed by properties of linear forms

Denis Belomestny — 2003

ESAIM: Probability and Statistics

Let ( X 1 , Y 1 ) , ... , ( X m , Y m ) be m independent identically distributed bivariate vectors and L 1 = β 1 X 1 + ... + β m X m , L 2 = β 1 Y 1 + ... + β m Y m are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of L 1 and L 2 imply the same property for X 1 and Y 1 , and under what conditions does the independence of L 1 and L 2 entail independence of X 1 and Y 1 ? Some analytical sufficient conditions are obtained and it is shown that in general they can not be weakened.

Constraints on distributions imposed by properties of linear forms

Denis Belomestny — 2010

ESAIM: Probability and Statistics

Let () be independent identically distributed bivariate vectors and , are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of and imply the same property for and , and under what conditions does the independence of and entail independence of and ? Some analytical sufficient conditions are obtained...

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