🤖 AI Summary
本文研究了Poisson和Crofton多面体的体积、表面积分布问题，采用混合分布模型（含广义伽马分布）并通过随机模拟估计参数。
📝 Abstract
This note presents new findings 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. This note motivates the modeling of the distributions of these convex body functionals as mixture distributions and the essential inclusion of the generalized gamma distribution therein as mixture components. Finally, model parameters are estimated and models are selected based on extensive stochastic simulations of these random polytopes. This includes that for the first time, this note gives very accurate estimates of the side number probabilities for both the Poisson polyhedron and the Crofton polyhedron, as these are used as mixing weights in the distribution models.