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The skew-Cauchy distribution

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

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 49 (2000)
    Issue (Month): 3 (September)
    Pages: 285-290

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    Handle: RePEc:eee:stapro:v:49:y:2000:i:3:p:285-290

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    Related research

    Keywords: Skewed-Cauchy Truncated Cauchy Generalized skewed distributions;

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    Cited by:
    1. 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.
    2. Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
    3. 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.
    4. Fang, B. Q., 2003. "The skew elliptical distributions and their quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 298-314, November.
    5. Loperfido, Nicola, 2001. "Quadratic forms of skew-normal random vectors," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 381-387, October.
    6. 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.
    7. 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.
    8. Umbach, Dale, 2006. "Some moment relationships for skew-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 507-512, March.
    9. 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.
    10. Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(2), pages 389-401, June.
    11. Huang, Wen-Jang & Chen, Yan-Hau, 2007. "Generalized skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1137-1147, June.
    12. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    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. 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.

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