.cor_cauchy {mcgf}R Documentation

Calculate Cauchy correlation

Description

Calculate Cauchy correlation

Usage

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

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].

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.


[Package mcgf version 1.1.0 Index]