On Some Properties of the Unified Skew Normal Distribution
Like some other multivariate skew normal distributions, the unified skew normal (SUN) distribution preserves important properties of the normal distribution. In this article, we show that for a random vector with a unified multivariate skew normal distribution all column (row) full rank linear transformations are in the same family of distributions. Using this property, we provide a characterization for the SUN distribution. In addition, we show that the joint distribution of the independent SUN random vectors is again a SUN distributed random vector. With this property and closure under the linear transformation, we finally show the closure of sums of independent SUN random vectors, and as expected it belongs to the same family.
KeywordsUnified skew normal distribution Linear transformation Characterization Singular distribution Distribution of the sum
AMS 2000 Subject ClassificationPrimary 62H10 Secondary 62P20
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