| matern.gc {gcKrig} | R Documentation |
The Matern Correlation Function of Class corr.gc
Description
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.
Usage
matern.gc(range = NULL, kappa = 0.5, nugget = TRUE)
Arguments
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. |
Details
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.
Value
An object of class corr.gc representing the correlation component.
Author(s)
Zifei Han hanzifei1@gmail.com
References
Diggle, P. and Ribeiro, P.J. (2007) Model-based Geostatistics. Springer.