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Communications in Statistics - Theory and Methods Volume 33, 2004 - Issue 7
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Original Articles

A New Class of Skew-Normal Distributions

Reinaldo B. Arellano-Valle Departamento de Estadística, Facultad de Matemática, Pontificia Universidad Católica de Chile, Santiago, Chile
,
Héctor W. Gómez Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó, Chile
&
Fernando A. Quintana Departamento de Estadística, Facultad de Matemática, Pontificia Universidad Católica de Chile, Santiago, Chile; Departamento de Estadística, Facultad de Matemática, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, 782-0436 MACUL, Santiago, ChileCorrespondence[email protected]
Pages 1465-1480 | Published online: 15 Feb 2007
 
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Abstract

We introduce a new family of asymmetric normal distributions that contains Azzalini's skew-normal (SN) distribution as a special case. We study the main properties of this new family, showing in particular that it may be generated via mixtures on the SN asymmetry parameter when the mixing distribution is normal. This property provides a Bayesian interpretation of the new family.

Mathematic Subject Classification:

Acknowledgments

The first author is partially supported by grant FONDECYT 1040865. The second author is partially supported by grant MECESUP PUC-0103. The third author is partially supported by grant FONDECYT 1020712.

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