For the probabilities of large deviations of Gaussian random vectors an asymptotic expansion is derived. Based upon a geometric measure representation for the Gaussian law the interactions between global and local geometric properties both of the distribution and of the large deviation domain...

For the multivariate l1-norm symmetric distributions, which are generalizations of the n-dimensional exponential distribution with independent marginals, a geometric representation formula is given, together with some of its basic properties. This formula can especially be applied to a new...

Euclidean distance-based classification rules are derived within a certain nonclassical linear model approach and applied to elliptically contoured samples having a density generating function g. Then a geometric measure theoretical method to evaluate exact probabilities of correct...

The providing of pure water for human needs and irrigation is one of the most important problems of many countries in hot climate. Moreover waste water is not purified at all or insufficiently. Purified waste water could be used by mankind e.g. for irrigation in order to establish a closed water...