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In the literature on probability distributions there are several approaches for extending the multivariate normal distribution with the introduction of some sort of skewness. The largest group of contributions was initiated by Azzalini and Dalla Valle (1996) and Azzalini and Capitanio (1999) and generalizes the univariate skew-normal distribution studied by Azzalini (1985, 1986). These "Multivariate skew-normal distributions" are generated from a normal distribution either by conditioning on a truncated variable or by a convolution mechanism.
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