EffectiveRange: Effective range for some spatial correlation functions

In StempCens: Spatio-Temporal Estimation and Prediction for Censored/Missing Responses

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.

Details

The available isotropic spatial correlation functions are:

Exponential:

Corr(d) = exp{-d/φ},

Gaussian:

Corr(d) = exp{-(d/φ)^2},

Matern:

Corr(d) = 1/(2^(κ-1)Γ(κ))(d/φ)^κ K_κ(d/φ),

Power exponential:

Corr(d) = exp{-(d/φ)^κ},

Spherical:

Corr(d) = 1 - 1.5 d/φ + 0.5(d/φ)^3,

where d is the Euclidean distance between two observations, φ is the spatial scaling parameter, Γ(.) is the gamma function, κ is the smoothness parameter and K_κ(.) is the modified Bessel function of the second kind of order κ.

Value

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

Author(s)

Katherine L. Valeriano, Victor H. Lachos and Larissa A. Matos

Examples

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.

Example output

StempCens documentation built on Oct. 23, 2020, 7:28 p.m.