Directional distributions for multi-dimensional random point processes
Directional distributions for multi-dimensional random point processes
复制标题
多维随机点过程的方向分布
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
V. Schmidt
中科院分区：
文献类型：
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作者：
D. König;V. Schmidt
在生物学（组织学）、材料科学、生态学和其他领域中，有定向的颗粒聚集体，它们可以在各向异性点过程的帮助下随机建模。此外，距离依赖取向在实践中确实出现。随机点过程Φ的各向异性可用Φ的点对间的连接向量的方向来描述。长度不同的向量可以有不同的有利方向。为了研究这种效应，我们考虑Φ的一个给定点x和它的最近邻点之间的矢量方向，该最近邻点是在Φ的这些点中选择的，到该点的距离超过某个最小距离。通过这种方式，我们定义了一个依赖于距离的方向分布。此外，第二种类型的这样的方向分布被认为是基于计算的一些给定的球壳的扇区中的点的数量。假设Φ是平稳的，我们讨论了这些方向估计的渐近性质。
In biology (histology), material science, ecology and further areas there are oriented aggregates of particles which can be stochastically modelled with the help of anisotropic point processes. Furthermore, distance-dependent orientations do appear in practice. The anisotropies of a random point process Φ are described by the directions of vectors connecting pairs of points of Φ. Vectors, the lengths of which are of different size, can have different favoured directions. For investigating this effect we consider the direction of the vector between a given point x of Φ and its nearest neighbour chosen within those points of Φ the distance to which from a; exceeds some minimum distance. In this way we define a distance-dependent directional distribution. Moreover, a second type of such a directional distribution is considered which is based on counting the numbers of points in sectors of some given spherical shell. Assuming that Φ is stationary we discuss asymptotic properties of estimators of these directi...