The Neyman–Scott processes introduced so far assume a symmetric distribution for the positions of the offspring points and this makes them inappropriate for modelling the skewed and bimodal clustered patterns and is a hindrance in fitting them to data that exhibit skewness or bimodality. In this paper, we apply the bivariate alpha-skew-normal distribution to the locations of the offspring points and introduce a Neyman–Scott process that regulates skewness and bimodality shapes in clustered point patterns. For this process, we obtain closed forms of the pair correlation function and the third-order intensity reweighted product density function and by use of the composite likelihood method, we fit the model to data. To examine the goodness-of-fit of the presented model, we use a statistical test based on the combined global scaled MAD envelopes. The use of the introduced process to model a clustered point pattern is illustrated by application to the locations of a species of trees in a rainforest dataset.

到目前为止引入的Neyman-Scott过程假设后代点的位置对称分布，这使其不适合建模偏斜和双峰聚类模式，并且阻碍了将它们拟合到具有偏斜或双峰性的数据中。在本文中，我们将双变量α-偏态正态分布应用于后代点的位置，并介绍了Neyman-Scott过程，该过程调节聚类点模式中的偏度和双峰形状。在此过程中，我们获得了对相关函数和三阶强度重加权产品密度函数的闭合形式，并使用复合似然法将模型拟合到数据中。为了检查所提出模型的拟合优度，我们使用了基于组合的全球规模化MAD包络的统计检验。