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Currently displaying 1 – 2 of 2

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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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