Sample from a Matérn point process over a unit disk:

Sample from a Matérn point process over a unit ball:

Sample from a Matérn point process over a geo region:

Sample from a valid region whose dimension is equal to its embedding dimension:

Check the region conditions:

Sample from a Matérn point process in the region and visualize the points:

Simulate a point configuration from a Matérn point process:

Use the "FindClusters" method to estimate a point process model:

Compare the Ripley measure between the original process and the estimated model:

Pair correlation function of a Matérn point process:

Visualize the function with given parameter values:

PointCountDistribution is known:

Mean and variance:

Plot the PDF:

Simulate the distribution:

The probability density histogram:

Ripley's and Besag's for Matérn point process in 2D:

Ripley's of Matérn point process is larger than for a Poisson point process:

Compare to the Poisson point process:

Besag's of Matérn point process is larger than for a Poisson point process:

Compare to the Poisson point process:

Pair correlation of Matérn point process is larger than 1:

Compare to homogeneous Poisson point process:

The estimation algorithm splitting the point data into clusters may find a different cluster radius than in a model used to create a given point collection:

Estimate all the parameters:

Therefore, specifying a smaller cluster radius than is inferred from the data will result in the failure of finding a point process model: