On the uncertainty relation for positive definite probability densities

Statistics

Volumn 31, Issue 1, 1998, Pages 83-88

  Gneiting, Tilmann ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Dual density; Laue's constant; Normal scale mixture; Positive definite; Uncertainty principle

Indexed keywords

EID: 3843136345     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331889808802628     Document Type: Article

References (7)

1. Andrews, D. F. and Mallows, C. L. (1974). Scale mixtures of normal distributions. J. Roy. Statist. Soc. B, 36, 99-102.
2. Dreier, I. (1996). On the uncertainty principle for positive definite densities. Zeitschr.für Analysis und ihre Anwendungen, 15, 1015-1023.
3. Gneiting, T. (1997). Symmetric Positive Definite Functions With Applications in Spatial Statistics. Ph.D. Thesis, Universität Bayreuth, Bayreuth, Germany.
4. Lewis, T. (1976). Probability functions which are proportional to characteristic functions and the infinite divisibility of the von Mises distribution. In Perspectives in Probability and Statistics, edited by Gani, J., 19-28. Academic Press, London.
5. Rossberg, H.-J. (1990). Positive definite probability densities. Theory of Probability and Its Applications, 35, 169-174.
6. Rossberg, H.-J. (1991). Characterization of the standard normal probability density within the class of self-adjoint (self-reciprocal) densities. Statistics, 22, 651-654, 26, 387.
7. Rossberg, H.-J. (1995). Positive definite probability densities and probability distributions. J. Mathem. Sciences, 76, 2181-2197.