mcgf (version 1.1.1)

cor_exp: Calculate exponential correlation

Description

Calculate exponential correlation

Usage

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

Value

Correlations of the same dimension as x.

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.

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)