fit.exponential()

Description:

Fit an exponential variogram model to empirical variogram estimates.

Usage:

fit.exponential(variogram.obj, c0, ce, ae, type='c', iterations=10, tolerance=1e-06, plot.it=T, weighted=T)

Required arguments:

variogram.obj: a variogram object generated by variogram()

c0, ce, ae: initial estimates for the exponential variogram model

Optional arguments:

type: one of 'c' (classic), 'r' (robust), 'm' (median). Indicates to which type of empirical variogram estimate the model is to be fit.

iterations: the number of iterations of the fitting procedure to execute.

tolerance: the tolerance used to determine if model convergence has been achieved.

plot.it: if T, the variogram estimate will be plotted each iteration.

weighted: if T, the fit will be done using weighted least squares, where the weightes are given in Cressie (1991, p. 99)

Value:

A variogram.model object.

Notes:

fit.exponential uses an iterative, Gauss-Newton fitting algorithm to fit empirical variogram estimates to an exponential variogram model given by

When weighted is T, the regression is weighted by

where the numerator is the number of pairs of points in a given lag.

Examples:

> stations.v.m <- fit.exponential(stations.v, 18, 20, 75000)