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

Description

Internal function called by the Variog.fit and ProbForecastGOP functions when fitting a generalized Cauchy theoretical variogram to an empirical variogram via the method of Weighted Least Squares when the estimate of the nugget effect is held fixed.

Usage

gencauchy.variog.fn(v,variog,d,w)

Arguments

numeric vector with the variance, range, smoothness, and long-range parameters of the generalized Cauchy 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 generalized Cauchy variogram evaluated for a given set v of variance, range, smoothness, and long-range parameters. This is the function that is minimized to obtain estimates of the variance, range, smoothness, and long-range parameters of the generalized Cauchy variogram, when the nugget effect is held fixed.

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 generalized Cauchy variogram when fitting to an empirical variogram via Weighted Least Squares, keeping the nugget effect fixed. - Defaults - None.