FMvariogram: Fit Gaussian geostatistical variogram to spatial and temporal...

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

Fit Gaussian geostatistical variogram to spatial and temporal mark variogram functions

Description

Fit Gaussian geostatistical variogram to the obtained spatial and temporal mark variograms

Usage

FMvariogram(u, gmv)

Arguments

u	vector of spatial or temporal distance at which gsp and gte was computed and where it will be fit.
gmv	vector containing the values of \gamma estimated through gsp and gte.

Details

This function fit Gaussian geostatistical variogram to the obtained mark variogram through gsp and gte functions using the R package geoR Ribeiro and Diggle (2001).

Value

u	If u is missing, a vector of distances u at which gsp and gte is computed from 0 to until quarter of the maximum distance between the points in the pattern.
gmv	The fitted Gaussian geostatistical variogram.
Parameters	The nugget effects, sill and range fitted for a Gaussian geostatistical variogram to the obtained spatial and temporal mark variograms.

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.

Gonzalez, J. A., Rodriguez-Cortes, F. J., Cronie, O. and Mateu, J. (2016). Spatio-temporal point process statistics: a review. Spatial Statiscts. 18:505-544.

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. Spatial Statistics, 20:125-147.

Ribeiro, Jr., Diggle, P.J. (2001). geoR: A package for geostatistical analysis. R New 1, 2:14–18.

Examples

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

# A realisation of spatio-temporal double-cluster (ellipsoid) point processes
Xe <- stdcpp(lambp=20, a=0.12, b=0.09, c=0.07, mu=100)
plot(Xe$xyt)

# Spatial mark variogram function
outs <- gsp(Xe$xyt)

# R plot - Spatial mark variogram function
par(mfrow=c(1,1))
xl <- c(0,0.25)
yl <- c(min(0,outs$egsp,1/12),max(0,outs$egsp,1/12))
plot(outs$ds,outs$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(outs$ds,rep(1/12,length(outs$ds)),col=11)
points(0,0,col=11,cex=1.5)

# Model parameters estimated "by least squares fit of empirical variograms"
fitv <- FMvariogram(outs$ds,outs$egsp)
fitv$Parameters
lines(fitv$u,fitv$gv)

# Temporal mark variogram function
outt <- gte(Xe$xyt)

# R plot - Temporal mark variogram function
par(mfrow=c(1,1))
xl <- c(0,0.25)
yl <- c(min(0,outt$egte,1/6),max(0,outt$egte,1/6))
plot(outt$dt,outt$egte,type="l",xlab="t = time",ylab=expression(gamma[te](t)),
     xlim=xl,ylim=yl,col=1,cex.lab=1.5,cex.axis=1.5)
lines(outt$dt,rep(1/6,length(outt$dt)),col=11)
points(0,0,col=11,cex=1.5)

# Model parameters estimated "by least squares fit of empirical variograms"
fitv <- FMvariogram(outt$dt,outt$egte)
fitv$Parameters
lines(fitv$u,fitv$gv)
## End(Not run)

frajaroco/msfstpp documentation built on July 24, 2024, 6:34 a.m.