The SPP Procedure

Testing for Complete Spatial Randomness

The homogeneous Poisson point process serves as a reference model for a completely spatially random (CSR) point pattern. A homogeneous Poisson point process that has intensity $\lambda > 0$ has the following properties:

  • The number of points $N(X\cap W)$ that fall in any region W has a Poisson distribution whose mean is $\lambda \times |W|$, where $|W|$ denotes the area of W.

  • If $W_1$ and $W_2$ are disjoint sets, then $N(X\cap W_1)$ and $N(X\cap W_2)$ are independent random variables.

  • The $N(X\cap W)$ points within a study area W are independent and uniformly distributed.