A New Class of Skew-Normal Distributions

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.

Key Words:

• Asymmetry
• Kurtosis
• Skew-normal
• Skew-curved normal
• Skew-generalized normal distributions

Mathematic Subject Classification:

• Primary 60E05
• Secondary 62E10

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.