Constraints on distributions imposed by properties of linear forms
ESAIM: Probability and Statistics (2010)
- 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 (2010): 313-328. <http://eudml.org/doc/104310>.
@article{Belomestny2010,
abstract = {
Let (X1,Y1),...,(Xm,Ym) be m independent identically
distributed bivariate vectors
and
L1 = β1X1 + ... + βmXm, L2 = β1X1 + ... + βmXm
are two linear forms with positive coefficients.
We study two problems:
under what conditions does the equidistribution of L1 and L2
imply the same property for
X1 and Y1, and under what conditions does the independence of L1
and L2 entail independence
of X1 and Y1?
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.; equidistribution; linear forms; characteristic functions},
language = {eng},
month = {3},
pages = {313-328},
publisher = {EDP Sciences},
title = {Constraints on distributions imposed by properties of linear forms},
url = {http://eudml.org/doc/104310},
volume = {7},
year = {2010},
}
TY - JOUR
AU - Belomestny, Denis
TI - Constraints on distributions imposed by properties of linear forms
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 313
EP - 328
AB -
Let (X1,Y1),...,(Xm,Ym) be m independent identically
distributed bivariate vectors
and
L1 = β1X1 + ... + βmXm, L2 = β1X1 + ... + βmXm
are two linear forms with positive coefficients.
We study two problems:
under what conditions does the equidistribution of L1 and L2
imply the same property for
X1 and Y1, and under what conditions does the independence of L1
and L2 entail independence
of X1 and Y1?
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.; equidistribution; linear forms; characteristic functions
UR - http://eudml.org/doc/104310
ER -
References
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- N.G. Ushakov, Selected topics in Characteristic functions. VSP, Utrecht and Tokyo (1999). Zbl0999.60500
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