StempCens (version 1.1.0)

EffectiveRange: Effective range for some spatial correlation functions

Description

It computes the effective range for an isotropic spatial correlation function, which is commonly defined to be the distance from which the correlation becomes small, typically below 0.05.

Usage

EffectiveRange(cor = 0.05, phi, kappa = 0, Sp.model = "exponential")

Arguments

cor

effective correlation to check for. By default = 0.05.

phi

spatial scaling parameter.

kappa

smoothness parameter, required by the matern and power exponential functions. By default = 0.

Sp.model

type of spatial correlation function: 'exponential' for exponential, 'gaussian' for gaussian, 'matern' for matern, 'pow.exp' for power exponential and 'spherical' for spherical function, respectively. By default = exponential.

Value

The function returns the effective range, i.e., the approximate distance from which the spatial correlation is lower than cor.

Details

The available isotropic spatial correlation functions are:

Exponential:

\(Corr(d) = exp{-d/\phi}\),

Gaussian:

\(Corr(d) = exp{-(d/\phi)^2}\),

Matern:

\(Corr(d) = 1/(2^(\kappa-1)\Gamma(\kappa))(d/\phi)^\kappa K_\kappa(d/\phi)\),

Power exponential:

\(Corr(d) = exp{-(d/\phi)^\kappa}\),

Spherical:

\(Corr(d) = 1 - 1.5 d/\phi + 0.5(d/\phi)^3\),

where d is the Euclidean distance between two observations, \phi is the spatial scaling parameter, \Gamma(.) is the gamma function, \kappa is the smoothness parameter and K_\kappa(.) is the modified Bessel function of the second kind of order \kappa.

Examples

# NOT RUN {
phi <- 164.60
range1 <- EffectiveRange(0.05, phi, kappa=0, Sp.model="exponential")
range2 <- EffectiveRange(0.05, phi, kappa=1, Sp.model="pow.exp")
# Note that these functions are equivalent.
# }