Recurrence relations for bivariate t and extended skew-t distributions and an application to order statistics from bivariate t

Computational Statistics and Data Analysis

Volumn 53, Issue 12, 2009, Pages 4018-4027

  Jamalizadeh, A ^a   Mehrali, Y ^a   Balakrishnan, N ^b  

^a SHAHID BAHONAR UNIVERSITY OF KERMAN   (Iran)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BIVARIATE; BIVARIATE T-DISTRIBUTION; CUMULATIVE DISTRIBUTION FUNCTION; DEGREES OF FREEDOM; EXPLICIT EXPRESSIONS; INTEGRAL VALUES; LINEAR COMBINATION OF ORDER STATISTICS; LINEAR COMBINATIONS; MEAN VECTOR; ORDER STATISTICS; RECURRENCE RELATIONS; T DISTRIBUTION;

RECURSIVE FUNCTIONS;

DISTRIBUTION FUNCTIONS;

EID: 69449100953     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2009.07.018     Document Type: Article

References (24)

1. Arellano-Valle R.B., and Azzalini A. On the unification of families of skew-normal distributions. Scandinavian Journal of Statistics 33 (2006) 561-574
2. Arellano-Valle R.B., and Genton M.G. On the exact distribution of linear combinations of order statistics from dependent random variables. Journal of Multivariate Analysis 98 (2007) 1876-1894
3. Arellano-Valle R.B., and Genton M.G. On the exact distribution of the maximum of absolutely dependent random variables. Statistics & Probability Letters 78 (2008) 27-35
4. Arnold B.C., and Beaver R.J. Skew multivariate models related to hidden truncation and/or selective reporting (with discussions). Test 11 (2002) 7-54
5. Azzalini A. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12 (1985) 171-178
6. Azzalini A. Further results on a class of distributions which includes the normal ones. Statistica 46 (1986) 199-208
7. Azzalini A. The skew-normal distribution and related multivariate families. Scandinavian Journal of Statistics 32 (2005) 159-188
8. Azzalini A., and Capitanio A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society, Series B 65 (2003) 367-389
9. Azzalini A., and Dalla Valle A. The multivariate skew-normal distribution. Biometrika 83 (1996) 715-726
10. Balakrishnan N. Multivariate normal distribution and multivariate order statistics induced by ordering linear combinations. Statistics & Probability Letters 17 (1993) 343-350
11. Basu A.P., and Ghosh J.K. Identifiability of the multinormal and other distributions under competing risks model. Journal of Multivariate Analysis 8 (1978) 413-429
12. Bazan J.A., Bolfarine H., and Branco M. A skew item response model. Bayesian Analysis 1 (2006) 861-892
13. Behboodian J., Jamalizadeh A., and Balakrishnan N. A new class of skew-Cauchy distributions. Statistics & Probability Letters 76 (2006) 1488-1493
14. Chen M.-H., Dey D.K., and Shao Q.M. A new skewed link model for dichotomous quantal response data. Journal of the American Statistical Association 94 (1999) 1172-1186
15. Fang K.T., Kotz S., and Ng K.W. Symmetric Multivariate and Related Distributions (1990), Chapman & Hall, London
16. Genc A. A note on the distributions of linear functions of two ordered correlated normal random variables. Communications in Statistics-Theory and Methods 35 (2006) 989-995
17. Gupta S.S., and Pillai K.C.S. On linear functions of ordered correlated normal random variables. Biometrika 52 (1965) 367-379
18. Henze N.A. A probabilistic representation of the skew-normal distribution. Scandinavian Journal of Statistics 13 (1986) 271-275
19. Jamalizadeh A., and Balakrishnan N. On order statistics from bivariate skew-normal and skew-t distributions. Journal of Statistical Planning and Inference 138 (2008) 4187-4197
20. ν distributions, Journal of Statistical Planning and Inference (in press)
21. Jamalizadeh A., Khosravi M., and Balakrishnan N. Recurrence relations for distributions of a skew-t and a linear combination of order statistics from a bivariate-t. Computational Statistics & Data Analysis 53 (2009) 847-852
22. Loperfido N. A note on skew-elliptical distributions and linear functions of order statistics. Statistics & Probability Letters 78 (2008) 3184-3186
23. Nagaraja H.N. A note on linear functions of ordered correlated normal random variables. Biometrika 69 (1982) 284-285
24. Wiens D.P., Beaulieu P., and Loskot N.C. On the exact distribution of the sum of the largest n - k out of n normal random variables with differing means. Statistics 40 (2005) 165-173