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Generalized skew-elliptical distributions and their quadratic forms

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  • Marc Genton

    ()

  • Nicola Loperfido

    ()

Abstract

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File URL: http://hdl.handle.net/10.1007/BF02507031
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Bibliographic Info

Article provided by Springer in its journal Annals of the Institute of Statistical Mathematics.

Volume (Year): 57 (2005)
Issue (Month): 2 (June)
Pages: 389-401

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Handle: RePEc:spr:aistmt:v:57:y:2005:i:2:p:389-401

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Related research

Keywords: Elliptical distribution; invariance; kurtosis; selection model; skewness; weighted distribution;

References

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  1. Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
  2. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
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Citations

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Cited by:
  1. Loperfido, Nicola, 2013. "Skewness and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 93-99.
  2. Behboodian, J. & Jamalizadeh, A. & Balakrishnan, N., 2006. "A new class of skew-Cauchy distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1488-1493, August.
  3. Fang, B.Q., 2008. "Noncentral matrix quadratic forms of the skew elliptical variables," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1105-1127, July.
  4. A. Abtahi & M. Towhidi & J. Behboodian, 2011. "An appropriate empirical version of skew-normal density," Statistical Papers, Springer, vol. 52(2), pages 469-489, May.
  5. A. Ghalamfarsa Mostofi & M. Kharrati-Kopaei, 2012. "Bayesian nonparametric inference for unimodal skew-symmetric distributions," Statistical Papers, Springer, vol. 53(4), pages 821-832, November.
  6. Samuel Kotz & Donatella Vicari, 2005. "Survey of developments in the theory of continuous skewed distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 225-261.
  7. Adelchi Azzalini & Marc G. Genton & Bruno Scarpa, 2010. "Invariance-based estimating equations for skew-symmetric distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 275-298.
  8. Arellano-Valle, Reinaldo B. & Genton, Marc G. & Loschi, Rosangela H., 2009. "Shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 91-101, January.
  9. Wang, Tonghui & Li, Baokun & Gupta, Arjun K., 2009. "Distribution of quadratic forms under skew normal settings," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 533-545, March.
  10. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
  11. Ley, Christophe & Paindaveine, Davy, 2010. "Multivariate skewing mechanisms: A unified perspective based on the transformation approach," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1685-1694, December.
  12. Thomas R. Allen Corns & Stephen E. Satchell, 2010. "Modelling conditional heteroskedasticity and skewness using the skew-normal distribution," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 251-263.
  13. Adelchi Azzalini, 2012. "Selection models under generalized symmetry settings," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(4), pages 737-750, August.
  14. Victor Lachos & Vicente Cancho & Reiko Aoki, 2010. "Bayesian analysis of skew-t multivariate null intercept measurement error model," Statistical Papers, Springer, vol. 51(3), pages 531-545, September.
  15. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
  16. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer, vol. 7(3), pages 241-266, September.
  17. Reinaldo Arellano-Valle & Marc Genton, 2010. "An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(2), pages 363-381, April.
  18. Christophe Ley & Davy Paindaveine, 2010. "On Fisher information matrices and profile log-likelihood functions in generalized skew-elliptical models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 235-250.

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