spatstat (version 1.63-0)

repul.dppm: Repulsiveness Index of a Determinantal Point Process Model

Description

Computes a measure of the degree of repulsion between points in a determinantal point process model.

Usage

repul(model, …)
# S3 method for dppm
repul(model, …)

Arguments

model

A fitted point process model of determinantal type (object of class "dppm").

…

Ignored.

Value

A numeric value or a pixel image.

Details

The repulsiveness index \(\mu\) of a determinantal point process model was defined by Lavancier, Moller and Rubak (2015) as $$ \mu = \lambda \int (1- g(x)) \, dx $$ where \(\lambda\) is the intensity of the model and \(g(x)\) is the pair correlation function, and the integral is taken over all two-dimensional vectors \(x\).

Values of \(\mu\) are dimensionless. Larger values of \(\mu\) indicate stronger repulsion between points.

If the model is stationary, the result is a single number.

If the model is not stationary, the result is a pixel image (obtained by multiplying the spatially-varying intensity by the integral defined above).

References

Lavancier, F., Moller, J. and Rubak, E. (2015), Determinantal point process models and statistical inference. Journal of Royal Statistical Society: Series B (Statistical Methodology), 77, 853--877.

See Also

dppm

Examples

# NOT RUN {
  jpines <- residualspaper$Fig1
  
# }
# NOT RUN {
  fit <- dppm(jpines ~ 1, dppGauss)
  repul(fit)
# }