FMvariogram: Fit Gaussian geostatistical variogram to spatial and temporal...
In frajaroco/msfstpp: Mark summary functions for spatio-temporal point processes

Description Usage Arguments Details Value Author(s) References Examples

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

1	FMvariogram(u, gmv)

`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 γ estimated through `gsp` and `gte`.

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).

`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.

Francisco J. Rodriguez Cortes <cortesf@uji.es> https://fjrodriguezcortes.wordpress.com

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.

## 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)