Onα-Symmetric Multivariate Characteristic Functions

Journal of Multivariate Analysis

Volumn 64, Issue 2, 1998, Pages 131-147

  Gneiting, Tilmann ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

symmetric distribution, Askey's theorem, Bessel function, characteristic function, Fourier transform, multivariate unimodality, positive definite

Indexed keywords

EID: 0001535351     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1997.1713     Document Type: Article

References (24)

1. Askey R. Tech. Rep. 1973.
2. Askey R. Some characteristic functions of unimodal distributions. J. Math. Anal. Appl. 50:1975;465-469.
3. Berk R., Hwang J. T. Optimality of the least squares estimator. J. Multivariate Anal. 30:1989;245-254.
4. Boas R. P., Kac M. Inequalities for Fourier transforms of positive functions. Duke Math. J. 12:1945;189-206.
5. Bochner S., Chandrasekharan K. Fourier Transforms. 1949;Princeton Univ. Press, Princeton.
6. p. Ann. Inst. H. Poincaré Probab. Statist. 2:1966;231-259.
7. Cambanis S., Huang S., Simons G. On the theory of elliptically contoured distributions. J. Multivariate Anal. 11:1981;368-385.
8. Cambanis S., Keener R., Simons G. Onα J. Multivariate Anal. 13:1983;213-233.
9. Chanysheva A. Yu. Positive definite functions of a special form. Moscow Univ. Math. Bull. 45:1990;57-59.
10. Dharmadhikari S., Joag-Dev K. Unimodality, Convexity, and Applications. 1988;Academic Press, Boston.
11. Fang K.-T., Kotz S., Ng K. W. Symmetric Multivariate and Related Distributions. 1990;Chapman and Hall, London.
12. Feller W. An Introduction to Probability Theory and Its Applications. 1971;Wiley, New York.
13. Gradshteyn I. S., Ryzhik I. M. Table of Integrals, Series, and Products. 1994;Academic Press, Boston.
14. Isaacson E., Keller H. B. Analysis of Numerical Methods. 1966;Wiley, New York.
15. Kuritsyn Yu. G., Shestakov A. V. Onα Theory Probab. Appl. 29:1984;804-806.
16. Lévy P. Extensions d'un théorème de D. Dugué et M. Girault. Z. Wahrsch. verw. Gebiete. 1:1962;159-173.
17. ∞. Statist. Probab. Lett. 8:1989;255-260.
18. α-spaces, Technical University of Wroclaw, Wroclaw.
19. Richards D. St. P. Positive definite symmetric functions on finite dimensional spaces. I. Applications of the Radon transform. J. Multivariate Anal. 19:1986;280-298.
20. Schoenberg I. J. Metric spaces and completely monotone functions. Ann. of Math. 39:1938;811-841.
21. Williamson R. E. Multiply monotone functions and their Laplace transforms. Duke Math. J. 23:1956;189-207.
22. Zastavnyi V. P. Positive definite functions depending on a norm. Russian Math. Dokl. 46:1993;112-114.
23. Zastavnyi V. P. Positive definite functions depending on the norm. Russian J. Math. Phys. 1:1993;511-522.
24. Zolotarev V. M. Integral transformations of distributions and estimates of parameters of multidimensional spherically symmetric stable laws. Contributions to Probability. 1981;Academic Press, New York. p. 283-305.