matern.gc | 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 τ^2 is of the form:
ρ(h) = (1-τ^2)* (1/(2^(κ-1) * Γ(κ))) * ((h/φ)^κ) * K_{κ}(h/φ)
when h > 0 and ρ(h) = 1 when h = 0. Here phi is range parameter, kappa is the shape parameter and tau^2 is the nugget parameter. K_κ(…) 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.
powerexp.gc
, spherical.gc
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