A skew extension of the t-distribution, with applications

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 65, Issue 1, 2003, Pages 159-174

  Jones, M C ^a   Faddy, M J ^b  

^a OPEN UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Beta distribution; Likelihood inference; Robustness; Skewness; Student's t distribution

Indexed keywords

EID: 0037848605     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00378     Document Type: Article

References (28)

1. Abramowitz, M. and Stegun, I. A. (eds) (1965) Handbook of Mathematical Functions. New York: Dover Publications.
2. Arnold, B. C. and Groeneveld, R. A. (1995) Measuring skewness with respect to the mode. Am. Statistn, 49, 34-38.
3. Azzalini, A. (1985) A class of distributions which includes the normal ones. Scand. J. Statist., 12, 171-178.
4. Azzalini, A. and Capitanio, A. (2003) Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J. R. Statist. Soc. B, 65, in the press.
5. Barndorff-Nielsen, O. E. and Shephard, N. (2001) Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion). J. R. Statist. Soc. B, 63, 167-241.
6. Butler, R. J., McDonald, J. B., Nelson, R. D. and White, S. B. (1990) Robust and partially adaptive estimation of regression models. Rev. Econ. Statist., 72, 321-327.
7. Cacoullos, T. (1965) A relation between t and F distributions. J. Am. Statist. Ass., 60, 528-531; correction, 1249.
8. Cox, D. R. and Reid, N. (1987) Parameter orthogonality and approximate conditional inference (with discussion). J. R. Statist. Soc. B, 49, 1-39.
9. DiCiccio, T. J., Kass, R. E., Raftery, A. and Wasserman, L. (1997) Computing Bayes factors by combining simulation and asymptotic approximations. J. Am. Statist. Ass., 92, 903-915.
10. Fernández, C. and Steel, M. J. F. (1998) On Bayesian modelling of fat tails and skewness. J. Am. Statist. Ass., 93, 359-371.
11. Fernández, C. and Steel, M. J. F. (1999) Multivariate Student-t regression models: pitfalls and inference. Biometrika, 86, 153-167.
12. Fisher, R. A. (1915) Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10, 507-521.
13. Fraser, D. A. S. (1979) Inference and Linear Models. New York: McGraw-Hill.
14. Garvin, J. S. and McClean, S. I. (1997) Convolution and sampling theory of the binormal distribution as a prerequisite to its application in statistical process control. Statistician, 46, 33-47.
15. Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (1995) Bayesian Data Analysis. London: Chapman and Hall.
16. Gibbons, J. F. and Mylroie, S. (1973) Estimation of impurity profiles in ion-implanted amorphous targets using joined half-Gaussian distributions. Appl. Phys. Lett., 22, 568-569.
17. Hosking, J. R. M. (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J. R. Statist. Soc. B, 52, 105-124.
18. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, vol. 2, 2nd edn. New York: Wiley.
19. Jones, M. C. (2001a) A skew t distribution. In Probability and Statistical Models with Applications (eds C. A. Charalambides, M. V. Koutras and N. Balakrishnan), pp. 269-277. London: Chapman and Hall.
20. Jones, M. C. (2001b) Multivariate t and beta distributions associated with the multivariate F distribution. Metrika, 54, 215-231.
21. Lange, K. L., Little, R. J. A. and Taylor, J. M. G. (1989) Robust statistical modelling using the t distribution. J. Am. Statist. Ass., 84, 881-896.
22. Mudholkar, G. S. and Hutson, A. (2000) The epsilon-skew-normal distribution for analyzing near-normal data. J. Statist. Planng Inf., 83, 291-309.
23. Mukhopadhyay, S. and Vidakovic, B. (1995) Efficiency of linear Bayes rules for a normal mean: skewed priors class. Statistician, 44, 389-397.
24. O'Hagan, A. and Leonard, T. (1976) Bayes estimation subject to uncertainty about parameter constraints. Biometrika, 63, 201-202.
25. Prentice, R. L. (1975) Discrimination among some parametric models. Biometrika, 62, 607-614.
26. Sahu, S. K., Dey, D. K. and Branco, M. D. (2002) A new class of multivariate skew distributions with applications to Bayesian regression models. To be published.
27. Skates, S. J. (1993) On secant approximations to cumulative distribution functions. Biometrika, 80, 223-235.
28. Smith, R. L. and Naylor, J. C. (1987) A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Appl. Statist., 36, 358-369.