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January, 1976 Two Necessary Conditions on the Representation of Bivariate Distributions by Polynomials
Shu-Gwei Tyan, Haluk Derin, John B. Thomas
Ann. Statist. 4(1): 216-222 (January, 1976). DOI: 10.1214/aos/1176343355

Abstract

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.

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Shu-Gwei Tyan. Haluk Derin. John B. Thomas. "Two Necessary Conditions on the Representation of Bivariate Distributions by Polynomials." Ann. Statist. 4 (1) 216 - 222, January, 1976. https://doi.org/10.1214/aos/1176343355

Information

Published: January, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0322.62018
MathSciNet: MR391384
Digital Object Identifier: 10.1214/aos/1176343355

Subjects:
Primary: 62E10
Secondary: 42A60 , 60E05

Keywords: Bivariate distribution function , orthonormal polynomials

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 1 • January, 1976
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