# disc.sb: Discretization nodes of a Shapiro-Botha variogram model In npsp: Nonparametric Spatial Statistics

 disc.sb R Documentation

## Discretization nodes of a Shapiro-Botha variogram model

### Description

Computes the discretization nodes of a â€˜nonparametricâ€™ extended Shapiro-Botha variogram model, following Gorsich and Genton (2004), as the scaled roots of Bessel functions.

### Usage

``````disc.sb(nx, dk = 0, rmax = 1)
``````

### Arguments

 `nx` number of discretization nodes. `dk` dimension of the kappa function (`dk >= 1`, see Details below). `rmax` maximum lag considered.

### Details

If `dk >= 1`, the nodes are computed as:

`x_i = q_i/rmax; i = 1,\ldots, 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,\ldots, nx.`

### Value

A vector with the discretization nodes.

### References

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.

### See Also

`kappasb`, `fitsvar.sb.iso`.

### Examples

``````disc.sb( 12, 1, 1.0)

nx <- 1
dk <- 0
x <- disc.sb(nx, dk, 1.0)
h <- seq(0, 1, length = 100)
plot(h, kappasb(x * h, 0), type="l", ylim = c(0, 1))
abline(h = 0.05, lty = 2)
``````

npsp documentation built on May 29, 2024, 5:31 a.m.