cor_exp: Calculate exponential correlation

In mcgf: Markov Chain Gaussian Fields Simulation and Parameter Estimation

Calculate exponential correlation

Description

Calculate exponential correlation

Usage

cor_exp(x, c, gamma = 1/2, nugget = 0, is.dist = FALSE)

Arguments

x	A numeric vector, matrix, or array.
c	Smooth parameter, c>0.
gamma	Scale parameter, \gamma\in(0, 1/2]. Default is 1/2.
nugget	The nugget effect \in[0, 1].
is.dist	Logical; if TRUE, x is a distance matrix or an array of distance matrices.

Details

The exponential correlation function with scale parameter c and smooth parameter \gamma has the form

C(x)=(1-\text{nugget})\exp(-c|x|^{2\gamma})+\text{nugget}\cdot \delta_{x=0},

where \delta_{x=0} is 1 when x=0 and 0 otherwise.

Value

Correlations of the same dimension as x.

References

Diggle, P. J., Tawn, J. A., & Moyeed, R. A. (1998). Model-Based Geostatistics. Journal of the Royal Statistical Society. Series C (Applied Statistics), 47(3), 299–350.

See Also

Other correlation functions: cor_cauchy(), cor_fs(), cor_lagr_askey(), cor_lagr_exp(), cor_lagr_tri(), cor_sep(), cor_stat(), cor_stat_rs()

Examples

x <- matrix(c(0, 5, 5, 0), nrow = 2)
cor_exp(x, c = 0.01, gamma = 0.5)

x <- matrix(c(0, 5, 5, 0), nrow = 2)
cor_exp(x, c = 0.01, gamma = 0.5, nugget = 0.3, is.dist = TRUE)

mcgf documentation built on June 29, 2024, 9:09 a.m.