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...

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...

Predicting the number of outstanding claims (IBNR) is a central problem in actuarial loss reserving. Classical approaches like the Chain Ladder method rely on aggregating the available data in form of loss triangles, thereby wasting potentially useful additional claims information. A new...

The present paper combines nonlinear shrinkage with the Multivariate Generalized Hyperbolic (MGHyp) distribution to account for heavy tails in estimating the first and second moments in high dimensions. An Expectation-Maximization (EM) algorithm is developed that is fast, stable, and applicable...