Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
AntonAntonov`QuantileRegression`
QuantileEnvelope |
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Details and Options
Examples
(1)
Basic Examples
(1)
Here is a set of random 2D points:
In[1]:=
npoints=12000;data={RandomReal[{0,2Pi},npoints],RandomVariate[SkewNormalDistribution[0.6,0.3,4],npoints]};data=MapThread[#2*{Cos[#1],Sin[#1]}&,data];rmat=RotationMatrix[-Pi/2.5].DiagonalMatrix[{2,1}];data=Transpose[rmat.Transpose[data]];data=TranslationTransform[{-Norm[Abs[#]/3],0}][#]&/@data;sndData=Standardize[data];
Here is a plot of the generated points with a grid of x- and y-quantiles:
In[2]:=
ListPlot[sndData,PlotStyleGray,GridLinesMap[Quantile[#,Range[0,1,1/(20-1)]]&,Transpose[data]],AspectRatioAutomatic,PlotTheme"Detailed",ImageSizeMedium]
Out[2]=
Here we find quantile envelope points:
In[3]:=
qs={0.7,0.75,0.8,0.85,0.90,0.95,0.98,.99};qsPoints=
[sndData,qs,60];
 | QuantileEnvelope |
Here the data and quantile envelopes are plotted together:
In[4]:=
Block[{data=sndData},Show[{ListPlot[data,PlotStyleGray,AspectRatioAutomatic,PlotTheme"Detailed",GridLinesMap[Quantile[#,Range[0,1,1/(20-1)]]&,Transpose[data]],PlotLegendsSwatchLegend[Blend[{Blue,Red},Rescale[#1,{Min[qs],Max[qs]},{0,1}]]&/@qs,qs]],Graphics[{PointSize[0.005],Thickness[0.0025],MapThread[{Blend[{Blue,Red},Rescale[#1,{Min[qs],Max[qs]},{0,1}]],Tooltip[Line[Append[#2,#2〚1〛]],#1],Point[#2]}&,{qs,qsPoints}]}]},ImageSizeMedium]]
Out[4]=
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