Numerical evaluation of compound distributions is one of the centralnumerical tasks in insurance mathematics. Two widely used techniques are Panjer recursion and transform methods...

We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersections of the half-spaces associated with the coordinate hyperplanes of an orthogonal basis. We obtain results on...

Let (Xt)t[set membership, variant]R[phi] be a diffusion on which starts in x and assume that a stationary initial distribution exists with continouos density [pi]. Then where T(x-[var epsilon], x + [epsilon]) denotes the first exit time of (x - [var epsilon], x + [epsilon]) and Zx[epsilon]) is...

We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises–Fisher, the Watson and the angular Gaussian families. In addition to several special results we present a general approach to isotropic distribution...