gear (version 0.1.5)

cmod.std: Standard covariance models for geostatistical data.

Description

Creates a standard covariance model (cmodStd) object for geostatistical data.

Usage

cmod.std(model, psill, r, evar = 0, fvar = 0, par3 = 0.5)

Arguments

model

A standard semivariance model type.

psill

The partial sill of the model. Must be a postive number.

r

The range parameter r. Must be a positive number.

evar

The variance of the errors. Must be non-negative number. The default is 0.

fvar

The finescale variance (microscale error). Must be a non-negative number. The default is 0.

par3

The value of the third parameter for 3 parameter models. Must be a positive number. The default is 0.5.

Value

Returns a cmodStd object.

Details

The general form of the specified covariance function is psill * \(\rho\)(d; r) + (evar + fvar)*(d==0), where \(\rho\) is the covariance function of the parametric models.

For the exponential model, \(\rho\)(d; r) is exp(-d/r).

For the gaussian model, \(\rho\)(d; r) is exp(-d^2/r^2).

For the matern model, \(\rho\)(d; r) is 2^(1-par3)/gamma(par3)*sd^par3*besselK(sd, nu = par3), where sd = d/r.

For the amatern (alternative Matern) model, \(\rho\)(d; r) is 2^(1-par3)/gamma(par3)*sd^par3*besselK(sd, nu = par3), where sd = 2 * sqrt(par3) * d/r.

For the spherical model, \(\rho\)(d; r) is 1 - 1.5*sd + 0.5*(sd)^3 if d < r, and 0 otherwise, with sd = d/r.

For the wendland1 model, \(\rho\)(d; r) is (1 - sd)^4 * (4*sd + 1) if d < r, and 0 otherwise, with sd = d/r.

For the wendland2 model, \(\rho\)(d; r) is (1 - sd)^6 * (35*sd^2 + 18*sd + 3))/3 if d < r, and 0 otherwise, with sd = d/r.

For the wu1 model, \(\rho\)(d; r) is (1 - sd)^3 * (1 + 3*sd + sd^2) if d < r, and 0 otherwise, with sd = d/r.

For the wu2 model, \(\rho\)(d; r) is (1 - sd)^4*(4 + 16*sd + 12*sd^2 + 3*sd^3))/4 if d < r, and 0 otherwise, with sd = d/r.

For the wu3 model, \(\rho\)(d; r) is (1 - sd)^6 * (1 + 6*sd + 41/3*sd^2 + 12*sd^3 + 5*sd^4 + 5/6*sd^5) if d < r, and 0 otherwise, with sd = d/r.

References

Waller, L. A., & Gotway, C. A. (2004). Applied Spatial Statistics for Public Health Data. John Wiley & Sons.

See Also

covmat

Examples

# NOT RUN {
cmod.std(model = "exponential", psill = 1, r = 1) 
# }