cor_cauchy function

Calculate Cauchy correlation

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.

Returns

Correlations of the same dimension as x.

Details

The Cauchy correlation function with scale parameter $a$ and smooth parameter $\alpha$ has the form

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

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)

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()