Calculate Cauchy correlation
.cor_cauchy(x, a, alpha, nu = 1, nugget = 0)Correlations of the same dimension as x.
A numeric vector, matrix, or array.
Smooth parameter, \(a>0\).
Scale parameter, \(\alpha\in(0, 1]\).
Power parameter, \(\nu>0\). Default is 1.
The nugget effect \(\in[0, 1]\).
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.
Gneiting, T., and Schlather, M. (2004). Stochastic Models That Separate Fractal Dimension and the Hurst Effect. SIAM Review, 46(2), 269–282.