Advanced Search

Models of random sets and of point processes are introduced to simulate some specific clustering of points, namely on random lines in ${ℝ}^2$ and ${ℝ}^3$ and on random planes in ${ℝ}^3$. The corresponding point processes are special cases of Cox processes. The generating distribution function of the probability distribution of the number of points in a convex set $K$ and the Choquet capacity $T\left(K\right)$ are given. A possible application is to model point defects in materials with some degree of alignment. Theoretical results...