Computer Values of the Matern Correlation Function
This function computes values of the Matern correlation function for given distances and parameters.
matern(u, phi, kappa)
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. |
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.
A vector matrix or array, according to the argument u, with the
values of the Matern
correlation function for the given distances.
Paulo J. Ribeiro Jr. paulojus@leg.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.
cov.spatial for the correlation functions
implemented in geoR, and besselK for computation
of the Bessel functions.
#
# 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))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.