Abstract

In the real world, there are point patterns where the offspring points are asymmetrically scattered around the parent points and have skewness in their locations. However, the existing distributions for the offspring locations in Neyman-Scott processes are usually assumed to be without any skewness in the clusters. This paper introduces a generalization of the Thomas process where the offspring points have a skew-normal distribution. We derive the pair correlation and third order intensity reweighted product density functions for the proposed process and use the composite likelihood approach to estimate the parameters. The model is applied to three real data sets and using the envelopes test and the DCLF test it is shown that the model provides a better fit than the ordinary Thomas process to the data.

摘要

在现实世界中，存在一些点模式，其中后代点不对称地散布在父点周围，并且它们的位置存在偏斜。但是，通常假设 Neyman-Scott 过程中后代位置的现有分布在集群中没有任何偏斜。本文介绍了 Thomas 过程的推广，其中后代点具有偏正态分布。我们为所提出的过程推导出对相关性和三阶强度重新加权的产品密度函数，并使用复合似然法来估计参数。该模型应用于三个真实数据集，并使用包络检验和 DCLF 检验表明，该模型比普通的 Thomas 过程更适合数据。