Some properties of the unified skew-normal distribution

Reinaldo B. Arellano-Valle and Adelchi Azzalini ()
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Reinaldo B. Arellano-Valle: Pontificia Universidad Católica de Chile
Adelchi Azzalini: Università degli Studi di Padova

Statistical Papers, 2022, vol. 63, issue 2, No 6, 487 pages

Abstract: 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.

Keywords: Unified skew-normal distribution; Truncated multivariate normal distribution; Mardia’s measures of multivariate skewness and kurtosis; Log-concavity; Non-standard conditional distribution (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00362-021-01235-2

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