# Constraints on distributions imposed by properties of linear forms

ESAIM: Probability and Statistics (2003)

- Volume: 7, page 313-328
- ISSN: 1292-8100

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topBelomestny, Denis. "Constraints on distributions imposed by properties of linear forms." ESAIM: Probability and Statistics 7 (2003): 313-328. <http://eudml.org/doc/245879>.

@article{Belomestny2003,

abstract = {Let $(X_1,Y_1),\ldots ,(X_m,Y_m)$ be $m$ independent identically distributed bivariate vectors and $L_1=\beta _1X_1+\ldots +\beta _mX_m$, $L_2=\beta _1Y_1+\ldots +\beta _mY_m$ 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.},

author = {Belomestny, Denis},

journal = {ESAIM: Probability and Statistics},

keywords = {equidistribution; independence; linear forms; characteristic functions},

language = {eng},

pages = {313-328},

publisher = {EDP-Sciences},

title = {Constraints on distributions imposed by properties of linear forms},

url = {http://eudml.org/doc/245879},

volume = {7},

year = {2003},

}

TY - JOUR

AU - Belomestny, Denis

TI - Constraints on distributions imposed by properties of linear forms

JO - ESAIM: Probability and Statistics

PY - 2003

PB - EDP-Sciences

VL - 7

SP - 313

EP - 328

AB - Let $(X_1,Y_1),\ldots ,(X_m,Y_m)$ be $m$ independent identically distributed bivariate vectors and $L_1=\beta _1X_1+\ldots +\beta _mX_m$, $L_2=\beta _1Y_1+\ldots +\beta _mY_m$ 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.

LA - eng

KW - equidistribution; independence; linear forms; characteristic functions

UR - http://eudml.org/doc/245879

ER -

## References

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