This note on distributions of convex body functionals of the Poisson polyhedron; first accurate estimates of number-of-sides probabilities

The distributions of convex body functionals of the Poisson polyhedron - Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf, HZDR

The distributions of convex body functionals of the Poisson polyhedron

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This note presents new results on the distribution of the volume and surface area of both the Poisson polyhedron and the Crofton polyhedron. It also considers the distribution of the area of the Poisson polygon and the Crofton polygon in the plane. Based on the fact that, for a given number of sides, the mean width of these random polytopes follows a gamma distribution with known parameters, this note provides motivation for the essential inclusion of the generalized gamma distribution in the modeling of the distribution of the convex body functionals under consideration. Finally, model parameters are estimated and models are selected based on very extensive stochastic simulations of these random polytopes. This includes that in this note, for the first time, very accurate estimates of the number-of-sides probabilities are reported for both the Poisson polyhedron and the Crofton polyhedron.

Keywords: Poisson polyhedron; Poisson cell; Crofton cell; convex body functionals

Statistics for simulated assemblies of particles from mathematical models ROBIS: 40073 is cited by this (Id 40164) publication

Weighted Poisson cells as models for random convex polytopes ROBIS: 18699 is cited by this (Id 40164) publication

Data publication: Simulation results for standard statistics of Poisson and … ROBIS: 40088 is cited by this (Id 40164) publication

DistributionModelsPHT: Julia package for distribution models for statistics of … ROBIS: 40114 is cited by this (Id 40164) publication

RandomCells: Julia package for the generation of random convex polytopes ROBIS: 39819 is cited by this (Id 40164) publication

Data publication: Simulation results for standard statistics of Poisson and … RODARE: 3290 is cited by this (Id 40164) publication

DistributionModelsPHT: Julia package for distribution models for statistics of … RODARE: 3300 is cited by this (Id 40164) publication

RandomCells: Julia package for the generation of random convex polytopes RODARE: 3231 is cited by this (Id 40164) publication

Data publication: Simulation results for standard statistics of Poisson and … ROBIS: 40088 HZDR-primary research data are used by this (Id 40164) publication

Data publication: Simulation results for standard statistics of Poisson and … RODARE: 3290 HZDR-primary research data are used by this (Id 40164) publication

Contribution to WWW arXiv:2609.12514 [math.PR]: https:

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