Let $X$ and $Y$ be two unbounded random variables. Then two necessary conditions are proved concerning the structure of the bivariate distribution function of $X$ and $Y$ when it is expanded in the orthonormal polynomials of its marginal distributions. The first condition concerns the shrinking of the polynomial representation into a diagonal form, and the second is a generalization of the Sarmanov-Bratoeva theorem.
Publié le : 1976-01-14
Classification:
Bivariate distribution function,
orthonormal polynomials,
62E10,
60E05,
42A60
@article{1176343355,
author = {Tyan, Shu-Gwei and Derin, Haluk and Thomas, John B.},
title = {Two Necessary Conditions on the Representation of Bivariate Distributions by Polynomials},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 216-222},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343355}
}
Tyan, Shu-Gwei; Derin, Haluk; Thomas, John B. Two Necessary Conditions on the Representation of Bivariate Distributions by Polynomials. Ann. Statist., Tome 4 (1976) no. 1, pp. 216-222. http://gdmltest.u-ga.fr/item/1176343355/