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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 and it is shown that in general they can not be weakened.
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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