✦ LIBER ✦

On Gaussian-like densities of order greater than two

✍ Scribed by Peter K. Willett; John B. Thomas

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 496 KB
Volume: 324
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(87)90052-4

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✦ Synopsis

Any non-degenerate bivariate density can be written as an infinite series; however, this representation is often too general for practical use. Considerable attention has focussed on classes of densities, in particular, we note the class with polynomial series. We could consider this useful class to be a generalization of the Mehler expansion for the bivariate Gaussian density. Here we extend this heuristic and present a similar class of tri-and multivariate densities. We jind the corresponding series representation for the general-order Gaussian and develop a non-trivial class of densities with similar form. In addition, we show that this form is in some respect the simplest possible.

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