On the Distributions of Scan Statistics
研究了扫描统计量在实数区间上的分布，针对固定独立均匀点和泊松过程两种情况，提出了新的级数计算方法和递归近似，在低密度下比封闭公式更实用。
Abstract This article considers the distribution of the scan statistic over some interval of the real line, both for a fixed number of independent uniform points and for a Poisson process. It provides a new series method of calculating this distribution in the Poisson case and a simple self-contained recursive approximation in the fixed case. These results work best at low densities, which is precisely the case when the closed formulas are computationally impractical. The results are compared with values tabulated by Neff and Naus (1980) and with a recent approximation due to Naus (1982). There is also an explanation of why Naus's approximation is good in the Poisson case and a derivation of recursive bounds in the fixed case. Key Words: Poisson processClusteringStatistical mechanics