On a Theorem of T. Gneiting on α-Symmetric Multivariate Characteristic Functions

T. Gneiting (1998, J. Multivariate Analysis64, 131–147) proved a relation between the primitives of the classes Φd(2) and Φd(1) of 2- and 1-symmetric characteristic functions on Rd, respectively. We will give a straightforward proof of his relation, answering a question of his. To do this we use the...

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Bibliographic Details
Published in:Journal of multivariate analysis 2000-11, Vol.75 (2), p.269-278
Main Author: zu Castell, Wolfgang
Format: Article
Language:English
Subjects:
Distribution theory
Exact sciences and technology
Fourier analysis
generalized hypergeometric functions, α-symmetric characteristic functions, norm-dependent positive definite functions
Mathematical analysis
Mathematics
Multivariate analysis
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Special functions
Statistics
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Summary:T. Gneiting (1998, J. Multivariate Analysis64, 131–147) proved a relation between the primitives of the classes Φd(2) and Φd(1) of 2- and 1-symmetric characteristic functions on Rd, respectively. We will give a straightforward proof of his relation, answering a question of his. To do this we use the calculus of generalized hypergeometric functions.
ISSN:0047-259X
1095-7243
DOI:10.1006/jmva.2000.1911