Properties of the Coefficients in a Diagonal Series Expansion of a Bivariate Density.
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1975
- Accession Number
- ADA011666
Entities
People
- G. L. Wise
- J. B. Thomas
Organizations
- Princeton University