cor_fs() R function from [mcgf]

Calculate correlation for fully symmetric model


cor_fs(nugget = 0, c, gamma = 1/2, a, alpha, beta = 0, h, u)

Arguments

nugget: The nugget effect $\in[0, 1]$ .
c: Scale parameter of cor_exp, $c>0$ .
gamma: Smooth parameter of cor_exp, $\gamma\in(0, 1/2]$ .
a: Scale parameter of cor_cauchy, $a>0$ .
alpha: Smooth parameter of cor_cauchy, $\alpha\in(0, 1]$ .
beta: Interaction parameter, $\beta\in[0, 1]$ .
h: Euclidean distance matrix or array.
u: Time lag, same dimension as h.

Returns

Correlations of the same dimension as h and u.

Details

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.

Examples


h <- matrix(c(0, 5, 5, 0), nrow = 2)
u <- matrix(0, nrow = 2, ncol = 2)
cor_fs(c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.5, h = h, u = u)

h <- array(c(0, 5, 5, 0), dim = c(2, 2, 3))
u <- array(rep(0:2, each = 4), dim = c(2, 2, 3))
cor_fs(c = 0.01, gamma = 0.5, a = 1, alpha = 0.5, beta = 0.5, h = h, u = u)

References

Gneiting, T. (2002). Nonseparable, Stationary Covariance Functions for Space–Time Data, Journal of the American Statistical Association, 97:458, 590-600.

cor_fs function