Result: Constraints on distributions imposed by properties of linear forms

Title:
Constraints on distributions imposed by properties of linear forms
Authors:
Denis Belomestny
Source:
ESAIM: Probability and Statistics. 7:313-328
Publisher Information:
EDP Sciences, 2003.
Publication Year:
2003
Subject Terms:
Characteristic functions, other transforms, equidistribution, Characterization and structure theory of statistical distributions, independence, linear forms, 0101 mathematics, Characterization and structure theory for multivariate probability distributions, copulas, 01 natural sciences, characteristic functions
Document Type:
Academic journal Article
File Description:
application/xml
ISSN:
1262-3318
1292-8100
DOI:
10.1051/ps:2003014
Access URL:
https://www.esaim-ps.org/articles/ps/pdf/2003/01/ps127.pdf
http://www.numdam.org/item/10.1051/ps:2003014.pdf
http://www.numdam.org/articles/10.1051/ps:2003014/
https://www.esaim-ps.org/articles/ps/ref/2003/01/ps127/ps127.html
https://www.cambridge.org/core/journals/esaim-probability-and-statistics/article/constraints-on-distributions-imposed-by-properties-of-linear-forms/4B804F23E7208431DC08EAC5EF4D046D
https://eudml.org/doc/245879
Accession Number:
edsair.doi.dedup.....3ad5a7e28a76ba49ee1fb9c2325341d4
Database:
OpenAIRE

Further Information

Summary: Let \((X_1,Y_1),\dots,(X_m,Y_m)\) be \(m\) independent, identically distributed bivariate vectors and \(L_1 = \beta_1X_1 + \dots + \beta_mX_m\), \(L_2 = \beta_1Y_1 + \dots + \beta_mY_m\) 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.