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A new class of skew-Cauchy distributions

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  • Behboodian, J.
  • Jamalizadeh, A.
  • Balakrishnan, N.
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    Abstract

    We discuss here a new class of skew-Cauchy distributions, which is related to Azzalini's [1985. A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178] skew-normal distribution denoted by Z[lambda]~SN([lambda]). A random variable W[lambda] is said to have a skew-Cauchy distribution (denoted by SC([lambda])) with parameter [lambda][set membership, variant]R if , where Z[lambda]~SN([lambda]) and X~N(0,1) are independent. In this paper, we discuss some simple properties of W[lambda], such as its density, distribution function, quantiles and a measure of skewness. Next, a bivariate Cauchy distribution is introduced using which some representations and important characteristics of W[lambda] are presented.

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    Bibliographic Info

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

    Volume (Year): 76 (2006)
    Issue (Month): 14 (August)
    Pages: 1488-1493

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    Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1488-1493

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    Related research

    Keywords: Skew-normal Skew-Cauchy Bivariate Cauchy;

    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. 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.
    3. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 11(1), pages 7-54, June.
    4. Loperfido, Nicola, 2001. "Quadratic forms of skew-normal random vectors," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 381-387, October.
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    Cited by:
    1. Lui, Kung-Jong & Chang, Kuang-Chao, 2009. "Corrigendum to: "Testing homogeneity of risk difference in stratified randomized trials with noncompliance" [Comput. Statist. Data Anal. 53 (2008) 209-221]," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1529-1529, February.

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