Calculate correlation for fully symmetric model
.cor_fs(nugget, c, gamma = 1/2, a, alpha, beta = 0, h, u)Correlations of the same dimension as h and u.
The nugget effect \(\in[0, 1]\).
Scale parameter of cor_exp, \(c>0\).
Smooth parameter of cor_exp, \(\gamma\in(0, 1/2]\).
Scale parameter of cor_cauchy, \(a>0\).
Smooth parameter of cor_cauchy, \(\alpha\in(0, 1]\).
Interaction parameter, \(\beta\in[0, 1]\).
Euclidean distance matrix or array.
Time lag, same dimension as h.
The fully symmetric correlation function with interaction parameter
\(\beta\) has the form
$$C(\mathbf{h}, u)=\dfrac{1}{(a|u|^{2\alpha} + 1)}
\left((1-\text{nugget})\exp\left(\dfrac{-c\|\mathbf{h}\|^{2\gamma}}
{(a|u|^{2\alpha}+1)^{\beta\gamma}}\right)+
\text{nugget}\cdot \delta_{\mathbf{h}=\boldsymbol 0}\right),$$
where \(\|\cdot\|\) is the Euclidean distance, and \(\delta_{x=0}\) is 1
when \(x=0\) and 0 otherwise. Here \(\mathbf{h}\in\mathbb{R}^2\) and
\(u\in\mathbb{R}\). By default beta = 0 and it reduces to the separable
model.
Gneiting, T. (2002). Nonseparable, Stationary Covariance Functions for Space–Time Data, Journal of the American Statistical Association, 97:458, 590-600.