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The skew-Cauchy distribution

Author

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  • Arnold, Barry C.
  • Beaver, Robert J.

Abstract

Suppose (X,Y) has a (k+1)-dimensional Cauchy distribution. Consider the conditional distribution of X given Y>y0, for some fixed value of . The resulting distribution is the multivariate skewed Cauchy, in which there is truncation with respect to Y: this is but one of a general class of skewed distributions for which the initial distribution is symmetric. The skewing function, which depends upon the distribution of Y, need not be from the same family as the initial density.

Suggested Citation

  • Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:3:p:285-290
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    Citations

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    Cited by:

    1. Loperfido, Nicola, 2001. "Quadratic forms of skew-normal random vectors," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 381-387, October.
    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., 2003. "The skew elliptical distributions and their quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 298-314, November.
    4. Hok Shing Kwong & Saralees Nadarajah, 2022. "A New Robust Class of Skew Elliptical Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1669-1691, September.
    5. Chung-Shin Liu & Meng-Shiuh Chang & Ximing Wu & Chin Man Chui, 2016. "Hedges or safe havens—revisit the role of gold and USD against stock: a multivariate extended skew- copula approach," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1763-1789, November.
    6. S. Cabras & M. E. Castellanos, 2009. "Default Bayesian goodness-of-fit tests for the skew-normal model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 223-232.
    7. 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.
    8. Alessandra Durio & Yacov Yu. Nikitin, 2001. "Local asympotic efficiency of some goodness-of-fit tests under skew alternatives," ICER Working Papers 04-2001, ICER - International Centre for Economic Research.
    9. 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.
    10. Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
    11. Alessandra Durio & Yakov Nikitin, 2002. "Asympotic efficiency of signed - rank symmetry tests under skew alternatives," ICER Working Papers 12-2002, ICER - International Centre for Economic Research.
    12. Yulia V. Marchenko & Marc G. Genton, 2010. "A suite of commands for fitting the skew-normal and skew-t models," Stata Journal, StataCorp LP, vol. 10(4), pages 507-539, December.
    13. Shakhatreh, M.K., 2012. "A two-parameter of weighted exponential distributions," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 252-261.
    14. Huang, Wen-Jang & Chen, Yan-Hau, 2006. "Quadratic forms of multivariate skew normal-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 871-879, May.
    15. Mahdy Mervat Mahdy Ramadan, 2011. "A Class of Weighted Gamma Distributions and its Properties," Stochastics and Quality Control, De Gruyter, vol. 26(2), pages 133-144, January.
    16. Umbach, Dale, 2006. "Some moment relationships for skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 507-512, March.
    17. Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 389-401, June.
    18. Vanduffel, Steven & Yao, Jing, 2017. "A stein type lemma for the multivariate generalized hyperbolic distribution," European Journal of Operational Research, Elsevier, vol. 261(2), pages 606-612.
    19. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    20. Jose, K.K. & Naik, Shanoja R., 2008. "A class of asymmetric pathway distributions and an entropy interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(28), pages 6943-6951.
    21. Zaid Mundher, 2022. "A Method for Investigating Coverage Area Issue in Dynamic Networks," Technium, Technium Science, vol. 4(1), pages 19-27.
    22. Huang, Wen-Jang & Chen, Yan-Hau, 2007. "Generalized skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1137-1147, June.

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