Volume 7, March 2003
|Page(s)||313 - 328|
|Published online||15 May 2003|
Constraints on distributions imposed by properties of linear forms
Institute fur Angewandte Mathematik, Universität Bonn,
Interdisziplinares Zentrum für Komplexe Systeme, Meckenheimer Allee 176,
53115 Bonn, Germany; firstname.lastname@example.org.
Revised: 17 March 2003
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.
Mathematics Subject Classification: 62E10 / 60E10
Key words: Equidistribution / independence / linear forms / characteristic functions.
© EDP Sciences, SMAI, 2003
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