Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Quantile Regression functions
Contributed by: Anton Antonov
Various Quantile Regression functions.
Installation Instructions
To install this paclet in your Wolfram Language environment,
evaluate this code:
PacletInstall["AntonAntonov/QuantileRegression"]
To load the code after installation, evaluate this code:
Needs["AntonAntonov`QuantileRegression`"]
Details
QuantileRegression works on time series, lists of numbers and lists of numeric pairs.
The curves computed with quantile regression are called regression quantiles.
The regression quantiles corresponding to the specified probabilities are linear combinations of B-splines generated over the specified knots.
In other words, QuantileRegression computes fits using a B-spline functions basis. The basis is specified with the knots argument and the option InterpolationOrder.
QuantileRegression takes the following options:
| InterpolationOrder | 3 | interepolation order |
| Method | LinearProgramming | method for the quantile regression computations |
QuantileRegressionFit is very similar to QuantileRegression but uses a given list of basis functions.
QuantileEnvelope provides experimental implementation of quantile envelopes points finding.
QuantileEnvelopeRegion provides experimental implementation of 2D or 3D quantile envelope region finding.
Paclet Guide
Examples
Basic Examples (5)
Make a random signal:
| In[1]:= | ![SeedRandom[23];
n = 200;
randData = Transpose[{Range[n], RandomReal[{0, 100.}, n]}];](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/7036842bd61c17c1.png) |
Compute QuantileRegression with five knots for the probabilities 0.25 and 0.75:
| In[2]:= | ![qFuncs = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], List[20.928985595703125`, 112.91769218444824`], List[21.882003784179688`, 111.26669120788574`], List[23.428985595703125`, 110.37369346618652`], List[197.5`, 9.87369155883789`], List[198.27300024032593`, 9.426692008972168`], List[199.13700008392334`, 9.203690528869629`], List[200.`, 9.203690528869629`], List[200.86299991607666`, 9.203690528869629`], List[201.72699999809265`, 9.426692008972168`], List[202.5`, 9.87369155883789`], List[376.5710144042969`, 110.37369346618652`], List[378.1179962158203`, 111.26669120788574`], List[379.0710144042969`, 112.91769218444824`], List[379.0710144042969`, 114.70369529724121`], List[379.0710144042969`, 315.7036876678467`], List[379.0710144042969`, 317.4896984100342`], List[378.1179962158203`, 319.1406993865967`], List[376.5710144042969`, 320.03370475769043`]]]]], List[FaceForm[List[RGBColor[0.5529411764705883`, 0.6745098039215687`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[44.92900085449219`, 282.59088134765625`], List[181.00001525878906`, 204.0298843383789`], List[181.00001525878906`, 46.90887451171875`], List[44.92900085449219`, 125.46986389160156`], List[44.92900085449219`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6627450980392157`, 0.803921568627451`, 0.5686274509803921`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[355.0710144042969`, 282.59088134765625`], List[355.0710144042969`, 125.46986389160156`], List[219.`, 46.90887451171875`], List[219.`, 204.0298843383789`], List[355.0710144042969`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6901960784313725`, 0.5882352941176471`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[200.`, 394.0606994628906`], List[336.0710144042969`, 315.4997024536133`], List[200.`, 236.93968200683594`], List[63.928985595703125`, 315.4997024536133`], List[200.`, 394.0606994628906`]]]]]], List[Rule[BaselinePosition, Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, 15]]], StyleBox[RowBox[List["QuantileRegression", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"AntonAntonov/QuantileRegression\"", ",", "\"AntonAntonov`QuantileRegression`QuantileRegression\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["AntonAntonov/QuantileRegression", "AntonAntonov`QuantileRegression`QuantileRegression"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["AntonAntonov/QuantileRegression", "AntonAntonov`QuantileRegression`QuantileRegression"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][randData, 5, {0.25, 0.75}];](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/06405eab0fdbe99b.png){kind=small} |
Here are the formulas of the obtained regression quantiles:
| In[3]:= | ![Simplify /@ Through[qFuncs[x]]](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/707c47f6875d2269.png){kind=small} |
| Out[3]= |  |
Here is a plot of the original data and the obtained regression quantiles:
| In[4]:= | ![ListLinePlot[{randData, qFuncs[[1]] /@ randData[[All, 1]], qFuncs[[2]] /@ randData[[All, 1]]}, PlotLegends -> {"data", 0.25`, 0.75`}, PlotStyle -> {Thin, Thick, Thick}, PlotTheme -> "Detailed"]](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/3bf862ebfc7c9906.png){kind=small} |
| Out[4]= |  |
Find the fraction of the data points that are under the second regression quantile:
| In[5]:= | ![Length[Select[randData, #[[2]] < qFuncs[[2]][#[[1]]] &]]/
Length[randData] // N](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/28a91e378f70f6b6.png){kind=small} |
| Out[5]= |  |
The obtained fraction is close to the second probability, 0.75, given to QuantileRegression.
Scope (3)
Here is a quantile regression computation over a numerical vector:
| In[6]:= | ![vecData = Sin[Range[200]/6] + RandomReal[{-0.5, 0.5}, 200];
qFunc = First@InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], List[20.928985595703125`, 112.91769218444824`], List[21.882003784179688`, 111.26669120788574`], List[23.428985595703125`, 110.37369346618652`], List[197.5`, 9.87369155883789`], List[198.27300024032593`, 9.426692008972168`], List[199.13700008392334`, 9.203690528869629`], List[200.`, 9.203690528869629`], List[200.86299991607666`, 9.203690528869629`], List[201.72699999809265`, 9.426692008972168`], List[202.5`, 9.87369155883789`], List[376.5710144042969`, 110.37369346618652`], List[378.1179962158203`, 111.26669120788574`], List[379.0710144042969`, 112.91769218444824`], List[379.0710144042969`, 114.70369529724121`], List[379.0710144042969`, 315.7036876678467`], List[379.0710144042969`, 317.4896984100342`], List[378.1179962158203`, 319.1406993865967`], List[376.5710144042969`, 320.03370475769043`]]]]], List[FaceForm[List[RGBColor[0.5529411764705883`, 0.6745098039215687`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[44.92900085449219`, 282.59088134765625`], List[181.00001525878906`, 204.0298843383789`], List[181.00001525878906`, 46.90887451171875`], List[44.92900085449219`, 125.46986389160156`], List[44.92900085449219`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6627450980392157`, 0.803921568627451`, 0.5686274509803921`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[355.0710144042969`, 282.59088134765625`], List[355.0710144042969`, 125.46986389160156`], List[219.`, 46.90887451171875`], List[219.`, 204.0298843383789`], List[355.0710144042969`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6901960784313725`, 0.5882352941176471`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[200.`, 394.0606994628906`], List[336.0710144042969`, 315.4997024536133`], List[200.`, 236.93968200683594`], List[63.928985595703125`, 315.4997024536133`], List[200.`, 394.0606994628906`]]]]]], List[Rule[BaselinePosition, Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, 15]]], StyleBox[RowBox[List["QuantileRegression", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"AntonAntonov/QuantileRegression\"", ",", "\"AntonAntonov`QuantileRegression`QuantileRegression\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["AntonAntonov/QuantileRegression", "AntonAntonov`QuantileRegression`QuantileRegression"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["AntonAntonov/QuantileRegression", "AntonAntonov`QuantileRegression`QuantileRegression"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][vecData, 12, 0.5];
ListLinePlot[{vecData, qFunc[#] & /@ Range[Length[vecData]]}, PlotRange -> All, PlotTheme -> "Detailed", PlotLegends -> {"vector", "fit"}]](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/67b042013449d345.png) |
| Out[8]= |  |
Here is a quantile regression computation over a time series object:
| In[9]:= | ![finData = FinancialData["GE", {{2010, 1, 1}, {2019, 10, 15}, "Week"}];
qFunc = First@InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], List[20.928985595703125`, 112.91769218444824`], List[21.882003784179688`, 111.26669120788574`], List[23.428985595703125`, 110.37369346618652`], List[197.5`, 9.87369155883789`], List[198.27300024032593`, 9.426692008972168`], List[199.13700008392334`, 9.203690528869629`], List[200.`, 9.203690528869629`], List[200.86299991607666`, 9.203690528869629`], List[201.72699999809265`, 9.426692008972168`], List[202.5`, 9.87369155883789`], List[376.5710144042969`, 110.37369346618652`], List[378.1179962158203`, 111.26669120788574`], List[379.0710144042969`, 112.91769218444824`], List[379.0710144042969`, 114.70369529724121`], List[379.0710144042969`, 315.7036876678467`], List[379.0710144042969`, 317.4896984100342`], List[378.1179962158203`, 319.1406993865967`], List[376.5710144042969`, 320.03370475769043`]]]]], List[FaceForm[List[RGBColor[0.5529411764705883`, 0.6745098039215687`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[44.92900085449219`, 282.59088134765625`], List[181.00001525878906`, 204.0298843383789`], List[181.00001525878906`, 46.90887451171875`], List[44.92900085449219`, 125.46986389160156`], List[44.92900085449219`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6627450980392157`, 0.803921568627451`, 0.5686274509803921`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[355.0710144042969`, 282.59088134765625`], List[355.0710144042969`, 125.46986389160156`], List[219.`, 46.90887451171875`], List[219.`, 204.0298843383789`], List[355.0710144042969`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6901960784313725`, 0.5882352941176471`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[200.`, 394.0606994628906`], List[336.0710144042969`, 315.4997024536133`], List[200.`, 236.93968200683594`], List[63.928985595703125`, 315.4997024536133`], List[200.`, 394.0606994628906`]]]]]], List[Rule[BaselinePosition, Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, 15]]], StyleBox[RowBox[List["QuantileRegression", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"AntonAntonov/QuantileRegression\"", ",", "\"AntonAntonov`QuantileRegression`QuantileRegression\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["AntonAntonov/QuantileRegression", "AntonAntonov`QuantileRegression`QuantileRegression"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["AntonAntonov/QuantileRegression", "AntonAntonov`QuantileRegression`QuantileRegression"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][finData, 12, 0.5];
DateListPlot[{finData, {#, qFunc[#]} & /@ finData["Times"]}, Joined -> {False, True}, PlotLegends -> {"time series", "fit"}]](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/29c555a3f26ca73e.png) |
| Out[10]= |  |
Here we find are some randomly generated 2D points:
| In[11]:= | ![sndData = CompressedData["
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MJxvXW01KEcTmWL9XbUZLLZUb6WEMeGaRXhcvjLPBTZ41z1fwkP+x1xSjB4f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EfE5Dz+HT6bEhwrga8hjM1rJMKr89FW3I1GIpeuP2PwQ/gW2LgSzcToPbhu+
Ku1cwoJR/G9L3989wM0iPTZ9dhPz8j/FJqTw0CWwKIirLYNHZWXZumf60O/J
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Xf7qjC1JAbmtOgXVIYO4ONsqiT4shOtCBptCpGPMneNil2Y5FlWqEo6fkAFq
kVcsGhkHjcCwzs+GfJwYKswOedCC8W5XzHR+E+GhwoHw6WI+Nvppq/5ZQobP
dg+bhCdFQHb2osctY6JPrfNbfMLHcdGCqPLX4+D0VMeXnVmKzOAP9Z8MZDhA
vBqqXkvGvwzDXG6q8eGz5w7WcN8QPj7S6qz4RQwZF5jGZScEkLSHfdG3shD2
c9aaHTz4HmcCS0+uLWfjYVfCXHbmEAaefBAWLWfASlNNi1rlHsrtT0e35FDQ
s2BS/egKJq6MI539sZwKNq9YZy/xZUBz22oZN0tDryvnFRdlImAQdz3abF6H
Jpaqiw/2FcKzbS6+jEghPD+Y4+KUKEZb916Oz1oy6nIbBk69YYL8b+kuhr0E
xxdxD755J4ZLJYSGsIctOKD/e8Gh91NwKf2UvCP1O0ofemqbM0ZwwkC7IWWS
BzflkTcys5ohUNQeT5ALoSJvT47/oBieXexntZp0omqiCbl77RiMqhVpeBZP
wPPGZaHXCtqU/VutZ/0fMswP2vLU3mQMHd5vD/sqFmDMfcHVehIf1dLOp0Ws
eY2uWhXxMfF0ePuv36pzjTzoqTrqSWWx4L/xvbcaSArMXzHZm2w7BtHnEmIr
c6VYctZkfLDlNWbUrN7cXCUAI581J05sVKk5E415QXw6XL1GLPlyewI12uJD
2jqVnOTucqHpSmEq0e11kjcJiR8PUVc7d0Ak347O2T6FVn8GSKPNpsGtY4Gv
WFwLjy0IYf7UKTAhxSoPXIjfCdlEnww+3E1TGFW20MF0eXvZZn0BlFJLy9d1
DKFX8trPNdu74c6ReeVRhlL8qyTVViVMAsxgtlfjyVqsXR7Uf22eCAyDdZsu
hDBxUNvW8xXMqSlSr1gpf9EAZdNS94FUEVSop7t6ycfRZlirgnBZAC7nJeVp
Sj41zVgWnvhnBGt5oSJ50SAyDq9Lm4kTo/f3/MbquhlwmmuVWCvlQOmu8CWD
N3hom3Iu2EtSDQz32HlN9RLM2nzWjTxvDPdNXNDzO02D8SpmyttrA3jAZGbl
aQcxZBJYJr76fBzTK5SxRAIwLtdKaL4uhiupe84delSL/wNuuh7e
"];](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/16b37c04b6907df9.png){kind=small} |
Here 2D quantile envelopes are computed of the points:
| In[12]:= | ![qs = Range[0.7, 1, 0.05];
qsPoints = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], List[20.928985595703125`, 112.91769218444824`], List[21.882003784179688`, 111.26669120788574`], List[23.428985595703125`, 110.37369346618652`], List[197.5`, 9.87369155883789`], List[198.27300024032593`, 9.426692008972168`], List[199.13700008392334`, 9.203690528869629`], List[200.`, 9.203690528869629`], List[200.86299991607666`, 9.203690528869629`], List[201.72699999809265`, 9.426692008972168`], List[202.5`, 9.87369155883789`], List[376.5710144042969`, 110.37369346618652`], List[378.1179962158203`, 111.26669120788574`], List[379.0710144042969`, 112.91769218444824`], List[379.0710144042969`, 114.70369529724121`], List[379.0710144042969`, 315.7036876678467`], List[379.0710144042969`, 317.4896984100342`], List[378.1179962158203`, 319.1406993865967`], List[376.5710144042969`, 320.03370475769043`]]]]], List[FaceForm[List[RGBColor[0.5529411764705883`, 0.6745098039215687`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[44.92900085449219`, 282.59088134765625`], List[181.00001525878906`, 204.0298843383789`], List[181.00001525878906`, 46.90887451171875`], List[44.92900085449219`, 125.46986389160156`], List[44.92900085449219`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6627450980392157`, 0.803921568627451`, 0.5686274509803921`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[355.0710144042969`, 282.59088134765625`], List[355.0710144042969`, 125.46986389160156`], List[219.`, 46.90887451171875`], List[219.`, 204.0298843383789`], List[355.0710144042969`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6901960784313725`, 0.5882352941176471`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[200.`, 394.0606994628906`], List[336.0710144042969`, 315.4997024536133`], List[200.`, 236.93968200683594`], List[63.928985595703125`, 315.4997024536133`], List[200.`, 394.0606994628906`]]]]]], List[Rule[BaselinePosition, Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, 15]]], StyleBox[RowBox[List["QuantileEnvelope", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"AntonAntonov/QuantileRegression\"", ",", "\"AntonAntonov`QuantileRegression`QuantileEnvelope\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["AntonAntonov/QuantileRegression", "AntonAntonov`QuantileRegression`QuantileEnvelope"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["AntonAntonov/QuantileRegression", "AntonAntonov`QuantileRegression`QuantileEnvelope"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][sndData, qs, 20];](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/544bf4690c4ed9f1.png){kind=small} |
Here the envelopes are plotted together with the data:
| In[13]:= | ![Block[{data = sndData}, Show[{ListPlot[data, PlotStyle -> {PointSize[0.006], GrayLevel[0.65]}, AspectRatio -> 1, PlotTheme -> "Detailed", PlotLegends -> SwatchLegend[
Blend[{Blue, Red}, Rescale[#1, {Min[qs], Max[qs]}, {0, 1}]] & /@
qs, qs]], Graphics[{PointSize[0.005], Thickness[0.005], MapThread[{Blend[{Blue, Red}, Rescale[#1, {Min[qs], Max[qs]}, {0, 1}]], Tooltip[Line[Append[#2, #2[[1]]]], #1], Point[#2]} &, {qs, qsPoints}]}]}]]](https://www.wolframcloud.com/obj/resourcesystem/images/a95/a95b4763-7c94-432e-9f74-e7dafb653fb3/1-0-1/5e3dd4bf531a1742.png) |
| Out[13]= |  |
Publisher
Compatibility
Wolfram Language Version 13.0
External Links
Version History
- 1.0.7 – 20 May 2023
- 1.0.6 – 17 May 2023
- 1.0.5 – 17 May 2023
- 1.0.4 – 16 May 2023
- 1.0.3 – 13 May 2023
- 1.0.2 – 29 April 2023
- 1.0.1 – 29 April 2023
- 1.0.0 – 18 April 2023