# kappasb: Coefficients of an extended Shapiro-Botha variogram model In npsp: Nonparametric Spatial Statistics

 kappasb R Documentation

## Coefficients of an extended Shapiro-Botha variogram model

### Description

Computes the coefficients of an extended Shapiro-Botha variogram model.

### Usage

kappasb(x, dk = 0)


### Arguments

 x numeric vector (on which the kappa function will be evaluated). dk dimension of the kappa function.

### Details

If dk >= 1, the coefficients are computed as:

\kappa_d(x) = (2/x)^{(d-2)/2} \Gamma(d/2) J_{(d-2)/2}(x)

where J_p is the Bessel function of order p.
If dk == 0, the coefficients are computed as:

\kappa _\infty(x) = e^{-x^2}

(corresponding to a model valid in any spatial dimension).
NOTE: some authors denote these functions as \Omega_d.

### Value

A vector with the coefficients of an extended Shapiro-Botha variogram model.

### References

Shapiro, A. and Botha, J.D. (1991) Variogram fitting with a general class of conditionally non-negative definite functions. Computational Statistics and Data Analysis, 11, 87-96.

svarmod.sb.iso, besselJ.

### Examples

kappasb(seq(0, 6*pi, len = 10), 2)

curve(kappasb(x/5, 0), xlim = c(0, 6*pi), ylim = c(-1, 1), lty = 2)
for (i in 1:10) curve(kappasb(x, i), col = gray((i-1)/10), add = TRUE)
abline(h = 0, lty = 3)


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