R: Repulsiveness Index of a Determinantal Point Process Model

repul.dppm {spatstat} | R Documentation

## 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 class 'dppm'
    repul(model, ...)

### Arguments

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

### Details

The repulsiveness index mu of a determinantal point process model was defined by Lavancier, Moller and Rubak (2015) as

mu = lambda * integral[(1-g(x))]

where λ 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 μ 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).

### Value

A numeric value or a pixel image.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

### 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

      jpines <- residualspaper$Fig1

      fit <- dppm(jpines ~ 1, dppGauss)
      repul(fit)

[Package spatstat version 1.63-3 Index]