Weighted Poisson cells as models for random convex polytopes

We introduce a parametric family for random convex polytopes in Rd which allows for an easy generation of samples for further use, e. g., as random particles in materials modelling and simulation. The basic idea consists in weighting the Poisson cell, which is the typical cell of the stationary and isotropic Poisson hyperplane tessellation, by suitable geometric characteristics. Since this approach results in an exponential family, parameters can be efficiently estimated by maximum likelihood. This work has been motivated by the desire for a flexible model for random convex particles as can be found in many composite materials such as concrete or refractory castables.