stpp (version 2.0-8)

gsp: Spatial mark variogram function

Description

Computes an estimator of the spatial mark variogram function.

Usage

gsp(xyt,s.region,s.lambda,ds,ks="epanech",hs,correction="none",approach="simplified")

Value

egsp

A vector containing the values of \(\gamma_{sp}(r)\) estimated

ds

If ds is missing, a vector of distances u at which gsp(u) is computed from 0 to until quarter of the maximum distance between the points in the pattern.

kernel

A vector of names and bandwidth of the spatial kernel.

gsptheo

Value under the Poisson case is calculated considering \(\tau\)=max(xyt[,3])-min(xyt[,3]).

Arguments

xyt

Spatial coordinates and times \((x,y,t)\) of the point pattern.

s.region

Two-column matrix specifying polygonal region containing all data locations.

s.lambda

Vector of values of the spatial intensity function evaluated at the points \((x,y)\) in \(W\). If s.lambda is missing, the estimate of the spatial mark correlation function is computed as for the homogeneous case, i.e. considering \(n/|W|\) as an estimate of the spatial intensity under the parameter approach="standardised".

ds

A vector of distances u at which gsp(u) is computed.

ks

A kernel function for the spatial distances. The default is the "epanech" kernel. It can also be "box" for the uniform kernel, or "biweight".

hs

A bandwidth of the kernel function ks.

correction

A character vector specifying the edge-correction(s) to be applied among "isotropic", "border", "modified.border", "translate", "setcovf" and "none". The default is "none".

approach

A character vector specifying the approach to use for the estimation to be applied among "simplified" or "standardised". If approach is missing, "simplified" is considered by default.

Author

Francisco J. Rodriguez Cortes <[e-mail]> https://fjrodriguezcortes.wordpress.com

Details

By default, this command calculates an estimate of the spatial mark variogram function \(\gamma_[sp](r)\) for a spatio-temporal point pattern.

References

Baddeley, A., Rubak, E., Turner, R. (2015). Spatial Point Patterns: Methodology and Applications with R. CRC Press, Boca Raton.

Chiu, S. N., Stoyan, D., Kendall, W. S., and Mecke, J. (2013). Stochastic Geometry and its Applications. John Wiley & Sons.

Gabriel, E., Rowlingson, B., Diggle P J. (2013) stpp: an R package for plotting, simulating and analyzing Spatio-Temporal Point Patterns. Journal of Statistical Software. 53, 1-29.

Illian, J B., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. John Wiley and Sons, London.

Stoyan, D., Rodriguez-Cortes, F. J., Mateu, J., and Gille, W. (2017). Mark variograms for spatio-temporal point processes. Spatial Statistics. 20, 125-147.

Examples

## Not run:
#################

# A realisation of spatio-temporal homogeneous Poisson point processes
hpp <- rpp(lambda = 100, replace = FALSE)$xyt

# R plot
plot(hpp)

# This function provides an kernel estimator of the spatial mark variogram function
out <- gsp(hpp)

# R plot - Spatial mark variogram function
par(mfrow=c(1,1))
xl <- c(0,0.25)
yl <- c(0,max(out$gsptheo,out$egsp))
plot(out$ds,out$egsp,type="l",xlab="r = distance",ylab=expression(gamma[sp](r)),
                 xlim=xl,ylim=yl,col=1,cex.lab=1.5,cex.axis=1.5)
lines(out$ds,rep(out$gsptheo,length(out$ds)),col=11)

## End(Not run)