FitVariogramParameters - Maple Help

Interpolation[Kriging]

 FitVariogramParameters
 estimate the nugget, sill, and range parameters for a set of points and values

 Calling Sequence FitVariogramParameters(k)

Parameters

 k - a Kriging object

Description

 • 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.

Examples

 > $\mathrm{points},\mathrm{data}≔\mathrm{Interpolation}:-\mathrm{Kriging}:-\mathrm{GenerateSpatialData}\left(\mathrm{Spherical}\left(1,10,1\right)\right)$
 ${\mathrm{points}}{,}{\mathrm{data}}{≔}\begin{array}{c}\left[\begin{array}{cc}{0.814723686393179}& {0.706046088019609}\\ {0.905791937075619}& {0.0318328463774207}\\ {0.126986816293506}& {0.276922984960890}\\ {0.913375856139019}& {0.0461713906311539}\\ {0.632359246225410}& {0.0971317812358475}\\ {0.0975404049994095}& {0.823457828327293}\\ {0.278498218867048}& {0.694828622975817}\\ {0.546881519204984}& {0.317099480060861}\\ {0.957506835434298}& {0.950222048838355}\\ {0.964888535199277}& {0.0344460805029088}\\ {⋮}& {⋮}\end{array}\right]\\ \hfill {\text{30 × 2 Matrix}}\end{array}{,}\begin{array}{c}\left[\begin{array}{c}{-1.31317888309841}\\ {3.78399452938781}\\ {-4.07906747556730}\\ {2.81033657021080}\\ {3.07159908082332}\\ {0.128958765233144}\\ {-3.21737272238246}\\ {0.707245165710619}\\ {0.0877877303791926}\\ {0.937296621856498}\\ {⋮}\end{array}\right]\\ \hfill {\text{30 element Vector[column]}}\end{array}$ (1)
 > $k≔\mathrm{Interpolation}:-\mathrm{Kriging}\left(\mathrm{points},\mathrm{data}\right)$
 ${k}{≔}\left(\begin{array}{c}{Kriging intⅇrpolation obȷⅇct with 30 samplⅇ points}\\ {Variogram: Sphⅇrical\left(1.25259453854482,13.6487615617247,.5525536774\right)}\end{array}\right)$ (2)
 > $\mathrm{FitVariogramParameters}\left(k,\mathrm{Spherical}\right)$
 $\left[{1.25259453854482}{,}{13.6487615617247}{,}{0.552553677400000}\right]$ (3)

Compatibility

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