The FitVariogramParameters command uses the heuristics described below to estimate the variogram parameters given a set of data.

The distance between each pair of points and the difference between the associated values are calculated.

The nugget is estimated to be the 25th percentile of the differences.

The sill is estimated to be the maximum of:

the 75th percentile of the differences, and

the smallest nonzero difference.

The range is estimated to be the 50th percentile of the distances.

$\mathrm{points},\mathrm{data}≔\mathrm{Interpolation}:-\mathrm{Kriging}:-\mathrm{GenerateSpatialData}\left(\mathrm{Spherical}\left(1\,10\,1\right)\right)$

$\mathrm{points},\mathrm{data}≔\begin{array}{c}\left[\begin{array}{cc}0.814723686393179& 0.706046088019609\\ 0.905791937075619& 0.0318328463774207\\ 0.126986816293506& 0.276922984960890\\ 0.913375856139019& 0.0461713906311539\\ 0.632359246225410& 0.0971317812358475\\ 0.0975404049994095& 0.823457828327293\\ 0.278498218867048& 0.694828622975817\\ 0.546881519204984& 0.317099480060861\\ 0.957506835434298& 0.950222048838355\\ 0.964888535199277& 0.0344460805029088\\ ⋮& ⋮\end{array}\right]\\ \hfill \text{30 × 2 Matrix}\end{array},\begin{array}{c}\left[\begin{array}{c}\mathrm{-1.31317888309841}\\ 3.78399452938781\\ \mathrm{-4.07906747556730}\\ 2.81033657021080\\ 3.07159908082332\\ 0.128958765233144\\ \mathrm{-3.21737272238246}\\ 0.707245165710619\\ 0.0877877303791926\\ 0.937296621856498\\ ⋮\end{array}\right]\\ \hfill \text{30 element Vector[column]}\end{array}$

$k≔\mathrm{Interpolation}:-\mathrm{Kriging}\left(\mathrm{points}\,\mathrm{data}\right)$

$k≔\left(\begin{array}{c}\mathrm{Kriging\; int\ⅇrpolation\; obȷ\ⅇct\; with\; 30\; sampl\ⅇ\; points}\\ \mathrm{Variogram:\; Sph\ⅇrical(1.25259453854482,13.6487615617247,.5525536774)}\end{array}\right)$

$\mathrm{FitVariogramParameters}\left(k\,\mathrm{Spherical}\right)$

$\left[1.25259453854482\,13.6487615617247\,0.552553677400000\right]$

The Interpolation[Kriging][FitVariogramParameters] command was introduced in Maple 2018.

For more information on Maple 2018 changes, see Updates in Maple 2018.