matern.gc: The Matern Correlation Function of Class 'corr.gc'

In gcKrig: Analysis of Geostatistical Count Data using Gaussian Copulas

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 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.

Value

An object of class corr.gc representing the correlation component.

Author(s)

Zifei Han [e-mail]

References

Diggle, P. and Ribeiro, P.J. (2007) Model-based Geostatistics. Springer.

See Also

powerexp.gc, spherical.gc

gcKrig documentation built on July 3, 2022, 1:05 a.m.