matern.variog: Internal function used to estimate the nugget effect, variance, range, and smoothness parameters in the Whittle-Matern variogram. This function is called by the Variog.fit and ProbForecastGOP functions when fitting a parametric Whittle-Matern variogram to an empirical variogram via the method of Weighted Least Squares.

Description

Internal function called by the Variog.fit and the ProbForecastGOP functions when fitting a Whittle-Matern theoretical variogram to an empirical variogram via the method of Weighted Least Squares.

Usage

matern.variog(v,variog,d,w)

Arguments

numeric vector with the nugget effect, variance, range, and smoothness parameters of the Whittle-Matern variogram.

variog

numeric vector giving the values of the empirical variogram at distances given by the numeric vector d.

numeric vector giving the distances (or the bin midpoints) at which the empirical variogram has been computed.

numeric vector giving the weights to be used in the Weighted Least Squares, that is, the number of pairs of meteorological stations with distance falling in any given bin.

Value

The function returns the weighted least-square loss function relative to the empirical variogram and the theoretical Whittle-Matern variogram evluated for a given set v of nugget effect, variance, range, and smoothness parameters. This is the function that is minimized to obtain estimates of the nugget effect, variance, range, and smoothness parameters of the Whittle-Matern variogram.

Details

This function is an internal function that is used and called by the Variog.fit and ProbForecastGOP functions to estimate the parameters of a Whittle-Matern variogram when fitting to an empirical variogram via Weighted Least Squares. - Defaults - None.