Description Usage Arguments Details References See Also Examples
Computes the discretization nodes of a ‘nonparametric’ extended Shapiro-Botha variogram model, following Gorsich and Genton (2004), as the scaled roots of Bessel functions.
1 | disc.sb(nx, dk = 0, rmax = 1)
|
nx |
number of discretization nodes. |
dk |
dimension of the kappa function ( |
rmax |
maximum lag considered. |
If dk >= 1
, the nodes are computed as:
x_i = q_i/rmax; i = 1,…, nx,
where q_i are the first n roots of J_{(d-2)/2}, J_p is the Bessel function of order p and rmax is the maximum lag considered. The computation of the zeros of the Bessel function is done using the efficient algorithm developed by Ball (2000).
If dk == 0
(corresponding to a model valid in any spatial dimension),
the nodes are computed so the gaussian variogram models involved have
practical ranges:
r_i = 2 ( 1 + (i-1) ) rmax/nx; i = 1,…, nx.
Ball, J.S. (2000) Automatic computation of zeros of Bessel functions and other special functions. SIAM Journal on Scientific Computing, 21, 1458-1464.
Gorsich, D.J. and Genton, M.G. (2004) On the discretization of nonparametric covariogram estimators. Statistics and Computing, 14, 99-108.
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