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Some properties of the unified skew-normal distribution

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  • Reinaldo B. Arellano-Valle

    (Pontificia Universidad Católica de Chile)

  • Adelchi Azzalini

    (Università degli Studi di Padova)

Abstract

For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia’s measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.

Suggested Citation

  • Reinaldo B. Arellano-Valle & Adelchi Azzalini, 2022. "Some properties of the unified skew-normal distribution," Statistical Papers, Springer, vol. 63(2), pages 461-487, April.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:2:d:10.1007_s00362-021-01235-2
    DOI: 10.1007/s00362-021-01235-2
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    References listed on IDEAS

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