Properties of the Coefficients in a Diagonal Series Expansion of a Bivariate Density.
PRINCETON UNIV N J DEPT OF ELECTRICAL ENGINEERING
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Diagonal series expansions of bivariate densities in terms of orthonormal functions are considered. If the n-th orthonormal function is an n-th degree polynomial, the bivariate density belongs to the class lambda introduced by Barrett and Lampard. It is shown that, if a class lambda bivariate density has identical marginal densities with unbounded support, then the coefficient sequence must be a mement sequence. Averaging over a parameter in the coefficient sequence is considered and is used to derive two new class lambda bivariate densities. Also, the coefficients are related to some dependency measures.
- Statistics and Probability