# gencauchy.variog.fn: Internal function used to estimate the variance, range,... In ProbForecastGOP: Probabilistic weather forecast using the GOP method

## 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

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

## Arguments

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

## 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.

## 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.

## Author(s)

Berrocal, V. J. veroberrocal@gmail.com, Gel, Y., Raftery, A. E., Gneiting, T.

ProbForecastGOP documentation built on May 2, 2019, 3:42 a.m.