dot-cor_cauchy function

Calculate Cauchy correlation

.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 $\in[0, 1]$.

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.

References

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