Master Thesis Multivariate Skew-Normal Distributions and their Extremal Properties

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 the univariate case we review the sufficient conditions on π that determines the maximal domain of attraction. In this case we also point out the difficulties that arise in determining the rate of convergence of the partial maxima. For the multivariate setup we give sufficient conditions on the skewing functions such that pairwise asymptotic independence is obtained. Master Thesis at the Department of Mathematics, Swiss Federal Institute of Technology, ETH Zurich Supervisor: Prof. Dr. Paul Embrechts Advisors: Dr. Parthanil Roy Natalia Lysenko