Negative Binomial Quadrat Counts and Point Processes
论文探讨了负二项分布拟合样方计数数据时隐含的可加性假设，寻找具有负二项一维分布且满足平稳、遍历和有序性的点过程，但未能找到同时具备这三种性质的过程，并总结了当前知识状态和近似方法。
Implicit in the fitting of negative binomial distributions to quadrat count data is an assumption, based partly on additivity, that if the areas of the quadrats are systematically changed then the fitting of another negative binomial distribution would be appropriate. It is therefore of interest to exhibit suitable probability models for which consistency with the additivity can be demonstrated. This leads to a search for point processes with negative binomial one-dimensional distributions and in particular for such processes which are in addition stationary, ergodic, and orderly. The paper fails to exhibit any negative binomial point process possessing all three of these properties and the authors now believe that no such process exists. However, it summarizes the present state of knowledge, including some discussion of approximations, and attempts to clarify the problems involved in what seems a difficult area.