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A new class of skew-Cauchy distributions. (English) Zbl 1096.60011
Summary: We discuss here a new class of skew-Cauchy distributions, which is related to A. Azzalini’s skew-normal distribution [Scand. J. Stat., Theory Appl. 12, 171–178 (1985; Zbl 0581.62014)] denoted by Z λ SN(λ). A random variable W λ is said to have a skew-Cauchy distribution (denoted by SC(λ)) with parameter λR if W λ = dZ λ /|X|, where Z λ SN(λ) and XN(0,1) are independent. We discuss some simple properties of W λ , 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 λ are presented.
MSC:
60E05General theory of probability distributions