Journal
STATISTICAL PAPERS
Volume 63, Issue 2, Pages 461-487Publisher
SPRINGER
DOI: 10.1007/s00362-021-01235-2
Keywords
Unified skew-normal distribution; Truncated multivariate normal distribution; Mardia's measures of multivariate skewness and kurtosis; Log-concavity; Non-standard conditional distribution
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Funding
- Universita degli Studi di Padova within the CRUI-CARE Agreement
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The research fills in some unknown properties of the family of multivariate probability distributions, including expressions for moments up to the fourth order and Mardia's measures, as well as the log-concavity property of the distribution.
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.
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