matern | R Documentation |
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))
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