mcgf (version 1.1.1)

cor_cauchy: Calculate Cauchy correlation

Description

Calculate Cauchy correlation

Usage

cor_cauchy(x, a, alpha, nu = 1, nugget = 0, is.dist = FALSE)

Value

Correlations of the same dimension as x.

Arguments

x

A numeric vector, matrix, or array.

a

Smooth parameter, \(a>0\).

alpha

Scale parameter, \(\alpha\in(0, 1]\).

nu

Power parameter, \(\nu>0\). Default is 1.

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 Cauchy correlation function with scale parameter \(a\) and smooth parameter \(\alpha\) has the form $$C(x)=(1-\text{nugget})(a|x|^{2\alpha} + 1)^{-\nu}+\text{nugget}\cdot \delta_{x=0},$$ where \(\delta_{x=0}\) is 1 when \(x=0\) and 0 otherwise.

References

Gneiting, T., and Schlather, M. (2004). Stochastic Models That Separate Fractal Dimension and the Hurst Effect. SIAM Review, 46(2), 269–282.

See Also

Other correlation functions: cor_exp(), 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_cauchy(x, a = 1, alpha = 0.5)

x <- matrix(c(0, 5, 5, 0), nrow = 2)
cor_cauchy(x, a = 1, alpha = 0.5, nugget = 0.3, is.dist = TRUE)