Normal scale mixtures and dual probability densities

Journal of Statistical Computation and Simulation

Volumn 59, Issue 4, 1997, Pages 375-384

  Gneiting, Tilmann ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Dual density; Normal scale mixture; Random variate generation

Indexed keywords

EID: 0031324470     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659708811867     Document Type: Article

References (28)

1. Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H. and Tukey, J. W. (1472) Robust Estimates of Location. Princeton University Press. Princeton.
2. Andrews, D. F. and Mallows, C. L. (1974) Scale mixtures of normal distributions. J. Roy. Statist. Soc. Ser. B, 36, 99-102.
3. Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size. Proc. Roy. Soc. London Ser. A, 353, 401-419.
4. Barndorff-Nielsen, O. (1978) Hyperbolic distributions and distributions on hyperbolae. Scand. J. Statist., 5, 151-157.
5. Barndorff-Nielsen, O. (1996) Normal inverse Gaussian distributions and stochastic volatility modelling. Scand. J. Statist., 24, 1-13.
6. Barndorff-Nielsen, O. and Blaesild, P. (1981) Hyperbolic distributions and ramifications: contributions to theory and applications. In Taillie, C., Patil, G. P. and Baldessari, B. A. (Eds.): Statistical Distributions in Scientific Work, 4, 19-44. Reidel, Dordrecht.
7. Barndorff-Nielsen, O., Kent, J. and Sørensen, M. (1982) Normal variance-mean mixtures and z distributions. Internat. Statist. Rev., 50, 145-159.
8. Box, G. E. P. and Tiao, G. C. (1992) Bayesian Inference in Statistical Analysis. Wiley Classics Library edition. Wiley, New York.
9. Devroye, L. (1986) Non-Uniform Random Variate Generation. Springer, New York.
10. Devroye, L. (1990) A note on Linnik's distribution. Statist. Probab. Lett., 9, 305-306.
11. Dreier, I. (1996) On the uncertainty principle for positive definite densities. Z. Anal. Anwendungen, 15, 1015-1023.
12. Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. 2. Second edition. Wiley, New York.
13. Gneiting, T. (1997) On the uncertainty relation for positive definite probability densities. To appear in Statistics.
14. Good, I. J. (1995) Dual density functions. J. Statist. Comput. Simulation, 52, 193-194.
15. Gradshteyn, I. S. and Ryzhik, I. M. (1994) Table of Integrals, Series, and Products. Fifth edition. Academic Press, Boston.
16. Harkness, W. L. and Harkness, M. L. (1968) Generalized hyperbolic secant distribution. J. Amer. Statist. Assoc., 63, 329-337.
17. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994a) Continuous Univariate Distributions Vol. 1. Second edition. Wiley, New York.
18. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994b) Continuous Univariate Distributions, Vol. 2. Second edition. Wiley, New York.
19. Kelker, D. (1971) Infinite divisibility and variance mixtures of the normal distribution. Ann. Math. Statist., 42, 802-808.
20. Lange, R. and Sinsheimer, J. S. (1993) Normal/independent distributions and their applications in robust regression. J. Comput. Graph. Statist., 2, 175-198.
21. Liu, C. (1996) Bayesian robust multivariate linear regression with incomplete data. J. Amer. Statist. Assoc., 91, 1219-1227.
22. McKay, A. T. (1932) A Bessel function distribution. Biometrika, 24, 39-44.
23. Newcomb, S. (1886) A generalized theory of the combination of observations so as to obtain the best result. Amer. J. Math., 8, 343-366.
24. Rogers, W. H. and Tukey, J. W. (1972) Understanding some long-tailed distributions. Statist. Neerlandica, 26, 211-226.
25. Romanowski, M. (1979) Random Errors in Observation and the Influence of Modulation on Their Distribution. Verlag Konrad Wittwer, Stuttgart.
26. Rossberg, H.-J. (1990) Positive definite probability densities. Theory Probab. Appl., 35, 169-174.
27. Rydberg, T. (1996) The normal inverse Gaussian Levy process: simulation and approximation. Resarch Report 344, Department of Theoretical Statistics, Aarhus University. Revised version to appear in Comm. Statist. Stochastic Models.
28. West, M. (1987) On scale mixtures of normal distributions. Biometrika, 14, 646-648.