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Zbl 1096.60011
Behboodian, J.; Jamalizadeh, A.; Balakrishnan, N.
A new class of skew-Cauchy distributions. (English)
[J] Stat. Probab. Lett. 76, No. 14, 1488-1493 (2006). ISSN 0167-7152

Summary: We discuss here a new class of skew-Cauchy distributions, which is related to {\it A. Azzalini}'s skew-normal distribution [Scand. J. Stat., Theory Appl. 12, 171--178 (1985; Zbl 0581.62014)] denoted by $Z_\lambda\sim \text{SN}(\lambda)$. A random variable $W_\lambda$ is said to have a skew-Cauchy distribution (denoted by SC($\lambda$)) with parameter $\lambda\in R$ if $W_\lambda\overset\text{d}\to= Z_\lambda/|X|$, where $Z_\lambda\sim \text{SN}(\lambda)$ and $X\sim \text{N}(0,1)$ are independent. 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.

MSC 2000:: *60E05 General theory of probability distributions

Keywords: skew-normal; bivariate Cauchy

Citations: Zbl 0581.62014

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