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Generalized skew-Cauchy distribution

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  • Huang, Wen-Jang
  • Chen, Yan-Hau
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    Abstract

    In this work we investigate the generalized skew-symmetric distributions. Suppose Y is an absolutely continuous random variable symmetric about 0 with probability density function f and cumulative distribution function F. If a random variable X satisfies , then X is said to have a generalized skew distribution of F (or f). The generalized skew-Cauchy (GSC) distribution are considered and special examples of GSC distribution are presented. Some of these examples are generated from generalized skew-normal or generalized skew-t distributions.

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    Bibliographic Info

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

    Volume (Year): 77 (2007)
    Issue (Month): 11 (June)
    Pages: 1137-1147

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    Handle: RePEc:eee:stapro:v:77:y:2007:i:11:p:1137-1147

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    Related research

    Keywords: Skew-Cauchy distribution Skew-normal distribution Skew-symmetric distribution Skew-t distribution;

    References

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    1. Monica Chiogna, 1998. "Some results on the scalar Skew-normal distribution," Statistical Methods and Applications, Springer, vol. 7(1), pages 1-13, April.
    2. Gupta, Arjun K. & González-Farías, Graciela & Domínguez-Molina, J. Armando, 2004. "A multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 181-190, April.
    3. Loperfido, Nicola, 2002. "Statistical implications of selectively reported inferential results," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 13-22, January.
    4. Arjun Gupta & Truc Nguyen & Jose Sanqui, 2004. "Characterization of the skew-normal distribution," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(2), pages 351-360, June.
    5. 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.
    6. Wang, Jiuzhou & Boyer, Joseph & Genton, Marc G., 2004. "A note on an equivalence between chi-square and generalized skew-normal distributions," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 395-398, March.
    7. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    8. Loperfido, Nicola, 2001. "Quadratic forms of skew-normal random vectors," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 381-387, October.
    9. 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.
    10. Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
    11. Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
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