Weighted Poisson Cells as Models for Random Convex Polytopes

Article

DOI: 10.1007/s11009-013-9342-y

Cite this article as:
Ballani, F. & van den Boogaart, K.G. Methodol Comput Appl Probab (2014) 16: 369. doi:10.1007/s11009-013-9342-y

Abstract

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.

Keywords

Random polygon Random polyhedron Poisson cell Crofton cell Exponential family  Gibbs distribution 

AMS 2000 Subject Classifications

60D05 62B05 60G55 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Felix Ballani
    • 1
  • Karl Gerald van den Boogaart
    • 1
    • 2
  1. 1.Institute for StochasticsTU Bergakademie FreibergFreibergGermany
  2. 2.Helmholtz Institute Freiberg for Resource TechnologyFreibergGermany

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