Last data update: 2014.03.03
R: Computer Values of the Matern Correlation Function
Computer Values of the Matern Correlation Function
Description
This function computes values of the Matern
correlation function
for given distances and parameters.
Usage
matern(u, phi, kappa)
Arguments
u
a vector, matrix or array with values of the distances
between pairs of data locations.
phi
value of the range parameter phi .
kappa
value of the smoothness parameter kappa .
Details
The Matern model is defined as:
rho(u;phi,kappa) =(2^(kappa-1) Gamma(kappa))^(-1)
(u/phi)^κ K_κ(u/φ)
where phi and kappa are parameters and
K_κ(…) denotes the modified Bessel function of the third
kind of order kappa .
The family is valid for phi > 0 and kappa > 0 .
Value
A vector matrix or array, according to the argument u
, with the
values of the Matern
correlation function for the given distances.
Author(s)
Paulo J. Ribeiro Jr. paulojus@leg.ufpr.br ,
Peter J. Diggle p.diggle@lancaster.ac.uk .
See Also
cov.spatial
for the correlation functions
implemented in geoR , and besselK
for computation
of the Bessel functions.
Examples
#
# Models with fixed range and varying smoothness parameter
#
curve(matern(x, phi= 0.25, kappa = 0.5),from = 0, to = 1.5,
xlab = "distance", ylab = expression(rho(h)), lty = 2,
main=expression(paste("varying ", kappa, " and fixed ", phi)))
curve(matern(x, phi= 0.25, kappa = 1),from = 0, to = 1.5, add = TRUE)
curve(matern(x, phi= 0.25, kappa = 2),from = 0, to = 1.5, add = TRUE,
lwd = 2, lty=2)
curve(matern(x, phi= 0.25, kappa = 3),from = 0, to = 1.5, add = TRUE,
lwd = 2)
legend("topright", expression(kappa==0.5, kappa==1.5, kappa==2, kappa==3),
lty=c(2,1,2,1), lwd=c(1,1,2,2))
#
# Correlations with equivalent "practical range"
# and varying smoothness parameter
#
curve(matern(x, phi = 0.25, kappa = 0.5),from = 0, to = 1,
xlab = "distance", ylab = expression(gamma(h)), lty = 2,
main = "models with equivalent "practical" range")
curve(matern(x, phi = 0.188, kappa = 1),from = 0, to = 1, add = TRUE)
curve(matern(x, phi = 0.14, kappa = 2),from = 0, to = 1,
add = TRUE, lwd=2, lty=2)
curve(matern(x, phi = 0.117, kappa = 2), from = 0, to = 1,
add = TRUE, lwd=2)
legend("topright", expression(list(kappa == 0.5, phi == 0.250),
list(kappa == 1, phi == 0.188), list(kappa == 2, phi == 0.140),
list(kappa == 3, phi == 0.117)), lty=c(2,1,2,1), lwd=c(1,1,2,2))
Results