A new class of skew-Cauchy distributions
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.
Volume (Year): 76 (2006)
Issue (Month): 14 (August)
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- 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;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 7-54, June.
- 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.
- Arnold, Barry C. & Beaver, Robert J., 2000. "The skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 285-290, September.
- 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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