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Characterization of a class of bivariate distribution functions

Author

Listed:
  • Tyan, S.
  • Thomas, J. B.

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.

Suggested Citation

  • Tyan, S. & Thomas, J. B., 1975. "Characterization of a class of bivariate distribution functions," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 227-235, June.
    • Handle: RePEc:eee:jmvana:v:5:y:1975:i:2:p:227-235
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    Cited by:

    1. López Blázquez, F. & Salamanca Miño, B., 2014. "Maximal correlation in a non-diagonal case," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 265-278.
    2. Angelo Koudou, 1998. "Lancaster bivariate probability distributions with Poisson, negative binomial and gamma margins," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 95-110, June.

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