In this master thesis we explore skewed distributions extended from the normal distribution. A transition from the symmetric to an asymmetric setting is formulated for the univariate as well as the multivariate case. This is done by introducing an additional infinite-dimensional parameter, namely a skewing function π. Our main focus is on the extremal behavior of such skewed random vectors. For...

This article develops recurrence relations for integrals that relate the density of multivariate extended skew-normal (ESN) distribution, including well-known (SN) distribution introduced by Azzalini and Dalla-Valle popular normal distribution. These recursions offer a fast computation arbitrary order product moments truncated folded distributions with as byproduct. In addition to approach, we ...

A class of multivariate extended skew-t (E ST ) distributions is introduced and studied in detail, along with closely related families such as the subclass of extended skew-normal distributions. Besides mathematical tractability and modeling flexibility in terms of both skewness and heavier tails than the normal distribution, the most relevant properties of the E ST distribution include closure...

Bivariate clustered (correlated) data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model (LMM) framework with underlying normality assumptions of the random effects and within-subject errors. However, such normality assumptions might be questionable if the data set particularly exhibits skewness and heavy tails. Using a Bayesian paradigm...

In many real applications related with Geostatistics, medical imaging and material science, the real observations have asymmetric, and heavy-tailed multivariate distributions. These observations are spatially correlated and they could be modelled by the skew random fields. However, certain statistical analysis problems require giving analytical expectations of some integral geometric characteri...