Multivariate exponential power distributions as mixtures of normal distributions with Bayesian applications

Communications in Statistics - Theory and Methods

Volumn 37, Issue 6, 2008, Pages 972-985

  Gomez Sanchez Manzano E ^a   Gomez Villegas M A ^a   Marin J M ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Elliptical distribution; Elliptically contoured distribution; Gibbs sampler; Hierarchical Bayesian model; Montecarlo methods; Multivariate exponential power distribution; Scale mixture of normal distributions; Stable distribution

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; DISTRIBUTION FUNCTIONS; HIERARCHICAL SYSTEMS; MATHEMATICAL MODELS; MONTE CARLO METHODS; MULTIVARIABLE CONTROL SYSTEMS; NORMAL DISTRIBUTION; PARAMETER ESTIMATION; PROBABILITY;

ELLIPTICAL DISTRIBUTION; ELLIPTICALLY CONTOURED DISTRIBUTION; GIBBS SAMPLER; STABLE DISTRIBUTION;

BAYESIAN NETWORKS;

EID: 38949172719     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920701762754     Document Type: Article

References (29)

1. Andrews, D. R., Mallows, C. L. (1974). Scale mixture of normal distributions. J. Roy. Stat. Soc. Ser. B Stat. Methodol. 36:99-102.
2. Basu, S., Miccheli C. A., Olsen, P. (2001). Power exponential densities for the training and classification of acoustic feature vectors in speech recognition. J. Comput. Graph. Statist. 10(1):158-184.
3. Berger, J. (1975). Minimax estimation of location vectors for a wide class of densities. Ann. Statist. 3(6):1318-1328.
4. Bernardo, J. M., Smith, F. M. (1994). Bayesian Theory. Chichester: Wiley and Sons.
5. Box, G., Tiao, G. (1973). Bayesian Inference in Statistical Analysis. Reading: Addison-Wesley.
6. Choy, S. T. B., Smith, A. F. M. (1997). Hierarchical models with scale mixtures of normal distributions. Test 6(1):205-221.
7. Devroye, L. (1986). Non-Uniform Random Variate Generation. New York: Springer-Verlag.
8. Fang, K. T., Kotz, S., Ng, K. W. (1990). Symmetric Multivariate and Related Distributions. London: Chapman and Hall.
9. Feller, W. (1971). An Introduction to Probability Theory and Its Applications. New York: Wiley and Sons.
10. García-Dorado, M. A., Marin, J. M. (1998). Minimum distance estimation of mutational parameters for quantitative traits. Biometrics 54(3):214-230.
11. Godsill S. J. (2000). Inference in symmetric alpha-stable noise using MCMC and the slice sampler. Proc. IEEE Int. Conf Acoustics, Speech and Signal Processing VL3806-3809.
12. Gómez, E., Gómez-Villegas, M. A., Marín, J. M. (1998). A multivariate generalization of the power exponential family of distributions. Commun. Statist. Theory Methods 27:589-600.
13. Gómez, E., Gómez-Villegas, M. A., Marín, J. M. (2002). A matrix variate generalization of the power exponential family of distributions. Commun. Statist. Theory Methods 31(12):2167-2182.
14. Gómez, E., Gómez-Villegas, M. A., Marín, J. M. (2003). A survey on continuous elliptical vector distributions. Rev. Mat. Complut. 16:345-361.
15. Gómez-Sánchez-Manzano, E., Gómez-Villegas, M. A., Marín, J. M. (2006). Sequences of elliptical distributions and mixtures of normal distributions. J. Multivariate Anal. 97:295-310.
16. Johnson, N. L., Kotz, S., Balakrishnan, N. (1994). Continuous Univariate Distributions. Vol 1. New York: Wiley.
17. Lindsey J. K. (1999). Multivariate elliptically-contoured distributions for repeated measurements. Biometrics 56:1277-1280.
18. Mardia, K. V., Kent, J. T., Bibby, J. M. (1982). Multivariate Analysis. London: Academic Press.
19. Marin, J. M. (1998). Continuous Elliptical and Power Exponential Distributions with Applications to Linear Dynamic Models. PhD. thesis, Departamento de Estadística e Investigación Operativa, Universidad Complutense de Madrid, Spain.
20. Nadarajah, S. (2003). The Kotz-type distribution with applications. Statistics 37(4):341-358.
21. Nolan, J. P. (1997). Numerical calculation of stable densities and distribution functions. Commun. Statist. Stochastic Models 13:759-774.
22. R Development Core Team (2007). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. http://www.R-project.org, Vienna (Austria).
23. Santiago, E., Albornoz, J., Domínguez, A., Toro, M. A., López-Fanjul, C. (1992). The distribution of spontaneous mutations on quantitative traits and fitness in Drosophila melanogaster. Genetics 132:771-781.
24. Samorodnitsky, G., Taqqu, M. S. (2000). Stable Non-Gaussian Random Processes. Boca Raton: Chapman and Hall.
25. Smith, B. J. (2005). Bayesian Output Analysis Program (BOA), Version 1.1.5. The University of Iowa, http://www.public-health.uiowa.edu/boa.
26. Subbotin, M. (1923). On the law of frequency of errors. Mathematicheskii Sbornik 31:296-301.
27. The Math Works, Inc. (2006). (Natick, MA, USA.) Matlab. Natick.
28. Turelli, M. (1984). Heritable genetic variation via mutation-selection balance: Lerch's zeta meets abdominal bristle. Theor. Pop. Biol. 25:138-193.
29. West, M. (1987). On scale mixtures of normal distributions. Biometrika 74:646-648.