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...

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...

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...