Multivariate log-skew-elliptical distributions with applications to precipitation data

Environmetrics

Volumn 21, Issue 3-4, 2010, Pages 318-340

  Marchenko, Yulia V ^a,b   Genton, Marc G ^b  

^a StataCorp   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Climatic regions; Extreme events; Heavy tails; Log skew normal; Log skew t; Moments; Multivariate; Precipitation; Skewness

Indexed keywords

EXTREME EVENT; MULTIVARIATE ANALYSIS; PRECIPITATION (CLIMATOLOGY); PROBABILITY; SKEWNESS; STOCHASTICITY;

UNITED STATES;

EID: 77249113120     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.1004     Document Type: Article

References (32)

1. Arellano-Valle RB, Azzalini A. 2006. On the unification of families of skew-normal distributions. Scandinavian Journal of Statistics 33: 561-574.
2. Arellano-Valle RB, Azzalini A. 2008. The centred parametrization for the multivariate skew-normal distribution. Journal of Multivariate Analysis 99: 1362-1382.
3. Arellano-Valle RB, Branco MD, Genton MG. 2006. A unified view on skewed distributions arising from selections. The Canadian Journal of Statistics 34: 581-601.
4. Arellano-Valle RB, Genton MG. 2007. On the exact distribution of linear combinations of order statistics from dependent random variables. Journal of Multivariate Analysis 98: 1876-1894.
5. Arellano-Valle RB, Genton MG. 2009.Multivariateextendedskew-tdistributionsandrelatedfamilieswithapplications. Technical report # 080628, Texas A&M University.
6. Azzalini A. 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12: 171-178.
7. Azzalini A. 2005. The skew-normal distribution and related multivariate families (with discussion by Marc G. Genton and a rejoinder by the author). Scandinavian Journal of Statistics 32: 159-200.
8. Azzalini A. 2006. R package sn: The skew-normal and skew-t distributions (version 0.4-6). URL http://azzalini.stat.unipd.it/SN
9. Azzalini A, Capitanio A. 1999. Statistical applications of the multivariate skew-normaldistribution. JournaloftheRoyalStatistical Society Series B 61: 579-602.
10. Azzalini A, Capitanio A. 2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society Series B 65: 367-389.
11. Azzalini A, dal Cappello T, Kotz S. 2003. Log-skew-normal and log-skew-t distributions as models for family income data. Journal of Income Distribution 11: 12-20.
12. Azzalini A, Dalla Valle A. 1996. The multivariate skew-normal distribution. Biometrika 83: 715-726.
13. Azzalini A, Genton MG. 2008. Robust likelihood methods based on the skew-t and related distributions. International Statistical Review 76: 106-129.
14. Beirlant J, Goegebeur Y, Segers J, Teugels J.2004.StatisticsofExtremes:TheoryandApplications.JohnWiley&Sons:Chichester
15. Branco MD Dey DK 2001. A general class of multivariate skew-elliptical distributions. Journal of Multivariate Analysis 79: 99-113.
16. Capitanio A, Azzalini A, Stanghellini E. 2003. Graphical models for skew-normal variates. Scandinavian Journal of Statistics 30: 129-144.
17. Chai HS, Baily KR. 2008. Use of log-skew-normal distribution in analysis of continuous data with a discrete component at zero. Statistics in Medicine 27: 3643-3655.
18. Chakraborty B. 2001. On affine equivariant multivariate quantiles. Annals of the Institute of Statistical Mathematics 53: 380-403
19. Chaudhuri P. 1996. On a geometric notion of quantiles for multivariate data. Journal of the American Statistical Association 91: 862-872.
20. Crow EL, Shimizu K. 1988. Lognormal Distributions: Theory and Applications. Marcel Dekker: New York.
21. DallaValle A.2007.A test for the hypothesis of skew-normalityinapopulation. JournalofStatisticalComputationandSimulation 77: 63-77.
22. Fang K-T, Kotz S, Ng KW. 1990. Symmetric Multivariate and Related Distributions. Chapman & Hall: New York.
23. Genton MG. 2004. Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality. Chapman & Hall/CRC: Boca Raton.
24. Marchenko YV, Genton MG. 2009. A suite of commands for fitting the skew-normal and skew-t distributions. Stata Journal (in preparation).
25. Mardia KV. 1970. Measures of multivariate skewness and kurtosis with applications. Biometrika 36: 519-530.
26. Pewsey A. 2000. Problems of inference for Azzalini's skew-normal distribution. Journal of Applied Statistics 27: 859-770
27. Pewsey A. 2006.Some observations on a simplemeans of generatingskewdistributions.In AdvancesinDistributionTheory,Order Statistics, and Inference, Balakrishnan N, Castillo E, Sarabia JM (eds). Statistics for Industry and Technology, Birkhauser: Boston, MA; 75-84.
28. R Development Core Team. 2008. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing: Vienna, Austria, ISBN 3-900051-07-0.
29. Sartori N. 2006. Bias prevention of maximum likelihood estimates for scalar skew normal and skew t distributions. Journal of Statistical Planning and Inference 136: 4259-4275.
30. StataCorp. 2007. Stata Statistical Software: Release 10. StataCorp LP: College Station, TX.
31. Wilks D. S. 2006. Statistical Methods in the Atmospheric Sciences (2nd edn). Academic Press: New York.
32. Wilson PS, Toumi R. 2005. A fundamental probability distribution for heavy rainfall. Geophysical Research Letters 32: L14812. doi:10.1029/2005GL022465