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Definition and probabilistic properties of skew-distributions

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Author Info
Arellano-Valle, R. B.
del Pino, G.
San Martín, E.
Abstract

The univariate and multivariate skew-normal distributions have a number of intriguing properties. It is shown here that these hold for a general class of distributions, defined in terms of independence conditions on signs and absolute values. For this class, two stochastic representations become equivalent, one using conditioning on the positivity of a random vector and the other employing a vector of absolute values. General methods for computing moments and for obtaining the density function of a general skew-distribution are given. The case of spherical and elliptical distributions is briefly discussed.

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

Volume (Year): 58 (2002)
Issue (Month): 2 (June)
Pages: 111-121
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Handle: RePEc:eee:stapro:v:58:y:2002:i:2:p:111-121

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Keywords: Skew-distributions Skew-normal Spherical distributions Elliptical distributions Stochastic representations;

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  1. Samuel Kotz & Donatella Vicari, 2005. "Survey of developments in the theory of continuous skewed distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 225-261. [Downloadable!]
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