Characterization of a class of bivariate distribution functions

S. Tyan and J. B. Thomas

Journal of Multivariate Analysis, 1975, vol. 5, issue 2, 227-235

Abstract: 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.

Keywords: Bivariate; distribution; conditional; expectation; moment; sequence; orthonormal; polynomials (search for similar items in EconPapers)
Date: 1975
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Citations: View citations in EconPapers (2)

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