GeoCorrFct_Cop {GeoModels}

Spatial and Spatio-temporal correlation or covariance of (non) Gaussian random fields (copula models)

Description

The function computes the correlations of a spatial or spatio-temporal or a bivariate spatial Gaussian or non Gaussian copula randomm field with a given covariance model and a set of spatial (temporal) distances.

Usage

GeoCorrFct_Cop(x,t=NULL,corrmodel, 
model="Gaussian",copula="Gaussian",
distance="Eucl", param, radius=6371,
n=1,covariance=FALSE,variogram=FALSE)

Arguments

x

A set of spatial distances.

t

A set of (optional) temporal distances.

corrmodel

String; the name of a correlation model, for the description see the Section Details.

model

String; the type of RF. See GeoFit.

copula

String; the type of copula. The two options are Gaussian and Clayton.

distance

String; the name of the spatial distance. The default is Eucl, the euclidean distance. See GeoFit.

param

A list of parameter values required for the covariance model.

radius

Numeric; a value indicating the radius of the sphere when using covariance models valid using the great circle distance. Default value is the radius of the earth in Km (i.e. 6371)

n

Numeric; the number of trials in a (negative) binomial random fields. Default is 1.

covariance

Logic; if TRUE then the covariance is returned. Default is FALSE

variogram

Logic; if FALSE then the covariance/coorelation is returned. Otherwise the associated semivariogram is returned

Value

Returns a vector of correlations or covariances values associated to a given parametric spatial and temporal correlation models.

Author(s)

Moreno Bevilacqua, [e-mail],https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, [e-mail], https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, [e-mail],https://www.researchgate.net/profile/Christian-Caamano

Examples

library(GeoModels)

################################################################
###
### Example 1. Correlation of a (mean reparametrized) beta random field with underlying 
### Matern correlation model using Gaussian and Clayton copulas
###
###############################################################

# Define the spatial distances
x = seq(0,0.4,0.01)

# Correlation Parameters for Matern model 
CorrParam("Matern")
NuisParam("Beta2")
# corr Gaussian copula
param=list(smooth=0.5,sill=1,scale=0.2/3,nugget=0,mean=0,min=0,max=1,shape=0.5)
corr1= GeoCorrFct_Cop(x=x, corrmodel="Matern", param=param,copula="Gaussian",model="Beta2")

plot(corr1,ylab="corr",main="Gauss copula correlation",lwd=2)

# corr Clayton copula
param=list(smooth=0.5,sill=1,scale=0.2/3,nugget=0,mean=0,min=0,max=1,shape=0.5,nu=2)
corr2= GeoCorrFct_Cop(x=x, corrmodel="Matern", param=param,copula="Clayton",model="Beta2")
lines(x,corr2$corr,ylim=c(0,1),lty=2)

plot(corr1,ylab="corr",main="Clayton copula correlation",lwd=2)