matern.gc {gcKrig} | R Documentation |
corr.gc
The Matern correlation function in spatial statistics.
By default, range parameter is not available, so
this function is used for likelihood inference and spatial prediction in function mlegc
and predgc
.
Users need to specify the shape parameter kappa
and if the correlation model includes a nugget effect
nugget = TRUE
or not nugget = FALSE
.
When both range and nugget parameters are given,
the function is used for simulation with function simgc
in package gcKrig
.
matern.gc(range = NULL, kappa = 0.5, nugget = TRUE)
range |
a non-negative scalar of the range parameter in Matern correlation function. |
kappa |
a non-negative scalar of the shape parameter in the Matern correlation function. The default kappa = 0.5 corresponds to an exponential correlation model. |
nugget |
the nugget effect of the correlation function. If specified, it must be a scalar between 0 and 1. |
The Matern correlation function with a nugget \tau^2
is of the form:
\rho(h) =
\frac{1-\tau^2}{2^{\kappa-1}\Gamma(\kappa)}\Big(\frac{h}{\phi}\Big)^\kappa
K_{\kappa}\Big(\frac{h}{\phi}\Big)
when h > 0
and \rho(h) = 1
when h = 0
. Here
\phi
is range parameter, \kappa
is the shape parameter and
\tau^2
is the nugget parameter.
K_\kappa(\cdot)
denotes the modified Bessel function of the third
kind of order \kappa
.
An object of class corr.gc
representing the correlation component.
Zifei Han hanzifei1@gmail.com
Diggle, P. and Ribeiro, P.J. (2007) Model-based Geostatistics. Springer.