# NOT RUN {
library(CompRandFld)
library(RandomFields)
library(scatterplot3d)
set.seed(31231)
# Set the coordinates of the points:
x <- runif(100, 0, 10)
y <- runif(100, 0, 10)
coords<-cbind(x,y)
################################################################
###
### Example 1. Plot of covariance and variogram functions
### estimated from a Gaussian random field with exponent
### correlation. One spatial replication is simulated.
###
###
###############################################################
# Set the model's parameters:
corrmodel <- "exponential"
mean <- 0
sill <- 1
nugget <- 0
scale <- 2
# Simulation of the Gaussian random field:
data <- RFsim(coordx=coords, corrmodel=corrmodel, param=list(mean=mean,
sill=sill, nugget=nugget, scale=scale))$data
# Maximum composite-likelihood fitting of the Gaussian random field:
start<-list(scale=scale,sill=sill,mean=mean(data))
fixed<-list(nugget=nugget)
# Maximum composite-likelihood fitting of the random field:
fit <- FitComposite(data, coordx=coords, corrmodel=corrmodel,likelihood="Marginal",
type="Pairwise",start=start,fixed=fixed,maxdist=6)
# Results:
print(fit)
# Empirical estimation of the variogram:
vario <- EVariogram(data, x, y)
# Plot of covariance and variogram functions:
par(mfrow=c(1,2))
Covariogram(fit, show.cov=TRUE, show.range=TRUE,
show.vario=TRUE, vario=vario,pch=20)
################################################################
##
### Example 2. Plot of covariance and extremal coefficient
### functions estimated from a max-stable random field with
### exponential correlation. n idd spatial replications are
### simulated.
###
###############################################################
set.seed(1156)
# Simulation of the max-stable random field:
data <- RFsim(coordx=coords, corrmodel=corrmodel, model="ExtGauss", replicates=20,
param=list(mean=mean,sill=sill,nugget=nugget,scale=scale))$data
start=list(sill=sill,scale=scale)
# Maximum composite-likelihood fitting of the max-stable random field:
fit <- FitComposite(data, coordx=coords, corrmodel=corrmodel, model='ExtGauss',
replicates=20, varest=TRUE, vartype='Sampling',
margins="Frechet",start=start)
data <- Dist2Dist(data, to='sGumbel')
# Empirical estimation of the madogram:
vario <- EVariogram(data, coordx=coords, type='madogram', replicates=20)
# Plot of correlation and extremal coefficient functions:
par(mfrow=c(1,2))
Covariogram(fit, show.cov=TRUE, show.range=TRUE, show.extc=TRUE,
vario=vario, pract.range=84,pch=20)
################################################################
###
### Example 3. Plot of covariance and variogram functions
### estimated from a Gaussian spatio-temporal random field with
### double-exp correlation.
### One spatio-temporal replication is simulated.
###
###############################################################
# Define the spatial-coordinates of the points:
#x <- runif(20, 0, 1)
#y <- runif(20, 0, 1)
# Define the temporal sequence:
#time <- seq(0, 30, 1)
# Simulation of the spatio-temporal Gaussian random field:
#data <- RFsim(x, y, time, corrmodel="exp_exp",param=list(mean=mean,
# nugget=nugget,scale_s=0.5,scale_t=1,sill=sill))$data
# Maximum composite-likelihood fitting of the space-time Gaussian random field:
#fit <- FitComposite(data, x, y, time, corrmodel="exp_exp", maxtime=5,
# likelihood="Marginal",type="Pairwise", fixed=list(
# nugget=nugget, mean=mean),start=list(scale_s=0.2,
# scale_t=1, sill=sill))
# Empirical estimation of spatio-temporal covariance:
#vario <- EVariogram(data, x, y, time, maxtime=10)
# Plot of the fitted space-time covariace
#Covariogram(fit,show.cov=TRUE)
# Plot of the fitted space-time variogram
#Covariogram(fit,vario=vario,show.vario=TRUE)
# Plot of covariance, variogram and spatio and temporal profiles:
#Covariogram(fit,vario=vario,fix.lagt=1,fix.lags=1,show.vario=TRUE,pch=20)
################################################################
###
### Example 4. Plot of parametric and empirical lorelograms
### estimated from a Binary Gaussian random fields with
### exponential correlation. One spatial replication is
### simulated.
###
###############################################################
#set.seed(1240)
# Define the spatial-coordinates of the points:
#x <- seq(0,3, 0.1)
#y <- seq(0,3, 0.1)
# Simulation of the Binary Gaussian random field:
#data <- RFsim(x, y, corrmodel=corrmodel, model="BinaryGauss",
# threshold=0,param=list(nugget=nugget,mean=mean,
# scale=.6,sill=0.8))$data
# Maximum composite-likelihood fitting of the Binary Gaussian random field:
#fit <- FitComposite(data, x, y, corrmodel=corrmodel, model="BinaryGauss",
# maxdist=0.8, likelihood="Marginal", type="Pairwise",
# start=list(mean=mean,scale=0.1,sill=0.1))
# Empirical estimation of the lorelogram:
#vario <- EVariogram(data, x, y, type="lorelogram", maxdist=2)
# Plot of fitted and empirical lorelograms:
#Covariogram(fit, vario=vario, show.vario=TRUE, lags=seq(0.1,2,0.1),pch=20)
# }
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