# est.variogram: Variogram Estimator In sgeostat: An Object-Oriented Framework for Geostatistical Modeling in S+

## Description

Calculate empirical variogram estimates.

An object of class `variogram` contains empirical variogram estimates generated from a point object and a pair object. A variogram object is stored as a data frame containing six columns: `lags`, `bins`, `classic`, `robust`, `med`, and `n`. The length of each vector is equal to the number of lags in the pair object used to create the variogram object, say l. The `lags` vector contains the lag numbers for each lag, beginning with one (1) and going to the number of lags (l). The `bins` vector contains the spatial midpoint of each lag. The `classic`, `robust`, and `med` vectors contain the classical,

classic(h)= 1/n sum_(i,j)_in_N(h) (z(x_i)-z(x_j))^2

robust,

robust(h)=(1/n sum_(i,j)_in_N(h) sqrt(|z(x_i)-z(x_j)|) )^4/(0.457 + 0.494/n)

and median

med(h)=(med_(i,j)_in_N(h) sqrt(|z(x_i)-z(x_j)|) )^4/(0.457 + 0.494/n)

variogram estimates for each lag, respectively (see Cressie, 1993, p. 75). The `n` vector contains the number |N(h)| of pairs of points in each lag N(h).

## Usage

 `1` ```est.variogram(point.obj, pair.obj, a1, a2) ```

## Arguments

 `point.obj` a point object generated by `point()` `pair.obj` a pair object generated by `pair()` `a1` a variable to calculate semivariogram for `a2` an optional variable name, if entered cross variograms will be created between `a1` and `a2`

## Value

A variogram object:

 `lags` vector of lag identifiers `bins` vector of midpoints of each lag `classic` vector of classic variogram estimates for each lag `robust` vector of robust variogram estimates for each lag `med` vector of median variogram estimates for each lag `n` vector of the number of pairs in each lag

## References

http://www.gis.iastate.edu/SGeoStat/homepage.html

`point`, `pair`
 `1` ```maas.v<-est.variogram(maas.point,maas.pair,'zinc') ```