Skew-elliptical distributions for environmental data

We describe a flexible family of multivariate skew-elliptical distributions that can account for skewness, heavy tails, and and multimodality in the data. It is straightforward to simulate from this family which possesses several invariance properties. In particular, we show that the distribution of the sample autocovariance function in time series and of the sample variogram in spatial statistics do not depend on the skewness of these distributions. We then discuss the use of a certain type of skew-normal distributions in the Kalman filter. This later topic is ongoing work with Philippe Naveau.