Characterization of a class of bivariate distribution functions

Let FX,Y(x,y) be a bivariate distribution function and Pn(x), Qm(y), n, m = 0, 1, 2,..., the orthonormal polynomials of the two marginal distributions FX(x) and FY(y), respectively. Some necessary conditions are derived for the co-efficients cn, n = 0, 1, 2,..., if the conditional expectation E[Pn(X) [short parallel] Y] = cnQn(Y) holds for n = 0, 1, 2,.... Several examples are given to show the application of these necessary conditions.

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Year of publication:	1975
Authors:	Tyan, S. ; Thomas, J. B.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 5.1975, 2, p. 227-235
Publisher:	Elsevier
Keywords:	Bivariate distribution conditional expectation moment sequence orthonormal polynomials

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005093825