Exact Closed-Form Formulae for Linear and Circular Continuous Scan Statistics: $P_c(N-1;N,w)$, $P_c(3;N,w)$, and $P(3;N,w)$

Haowei Yuan

The continuous linear $P(k;N,w)$ and circular scan statistics $P_c(k;N,w)$ are fundamental tools in probability and spatial statistics, frequently used to detect clustering in…