Vmr: Spatial mark variance function

In frajaroco/msfstpp: Mark summary functions for spatio-temporal point processes

Description

Computes an estimator of the spatial variance mark function.

Usage

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

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 Vmr(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.

Details

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

Value

eVmr	A vector containing the values of V_[sp](u) estimated.
ds	If ds is missing, a vector of distances u at which Vmr(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.
vmrtheo	Value under the Poisson case is calculated considering τ=max(xyt[,3])-min(xyt[,3]).

Author(s)

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

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 Wilfried, G. (2016). Mark variograms for spatio-temporal point processes, Submitted .

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 variance mark function
out <- Vmr(hpp)

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

## End(Not run)

frajaroco/msfstpp documentation built on May 16, 2019, 1:52 p.m.