cor_cauchy: Calculate Cauchy correlation

In mcgf: Markov Chain Gaussian Fields Simulation and Parameter Estimation

Calculate Cauchy correlation

Description

Calculate Cauchy correlation

Usage

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

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.

Value

Correlations of the same dimension as x.

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)

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