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How do I merge a boxplot with distribution plot?

Alex Teymouri

Posted 10 months ago

Hi, How do I merge the distribution plot to the box plot in Mathematica like the below figure? Jan = {2.09, 0.9, 317.4, 472.400, 417.79, 234.200, 325., 524.2, 49.59, 114.7, 126.1, 136., 160.6, 203.2, 157.8, 0., 8., 23.5}; Feb = {0., 0., 0.5, 111.2, 155.700, 324.59, 152.5, 348.3, 222., 0., 0., 0., 0., 0., 24., 186., 118.3, 387.3}; BoxWhiskerChart[{Jan, Feb}, FrameLabel -> {"Month", "Discharge"}, ChartLabels -> {{"\!\(\* StyleBox[\"Jan\",\nFontSize->16]\)", "\!\(\* StyleBox[\"Feb\",\nFontSize->16]\)"}}]

Hi,

How do I merge the distribution plot to the box plot in Mathematica like the below figure?

Jan = {2.09, 0.9, 317.4, 472.400, 417.79, 234.200, 325., 524.2, 49.59,
    114.7, 126.1, 136., 160.6, 203.2, 157.8, 0., 8., 23.5};

Feb = {0., 0., 0.5, 111.2, 155.700, 324.59, 152.5, 348.3, 222., 0., 
   0., 0., 0., 0., 24., 186., 118.3, 387.3};

BoxWhiskerChart[{Jan, Feb}, FrameLabel -> {"Month", "Discharge"}, 
 ChartLabels -> {{"\!\(\*
StyleBox[\"Jan\",\nFontSize->16]\)", "\!\(\*
StyleBox[\"Feb\",\nFontSize->16]\)"}}]

POSTED BY: Alex Teymouri

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Jim Baldwin

Posted 10 months ago

A much better answer than mine is found at https://mathematica.stackexchange.com/questions/128214/update-combining-distributionchart-and-boxwhiskerchart.

POSTED BY: Jim Baldwin

Jim Baldwin

Posted 10 months ago

Here's a very ad hoc approach: Jan = {2.09, 0.9, 317.4, 472.400, 417.79, 234.200, 325., 524.2, 49.59, 114.7, 126.1, 136., 160.6, 203.2, 157.8, 0., 8., 23.5}; Feb = {0., 0., 0.5, 111.2, 155.700, 324.59, 152.5, 348.3, 222., 0., 0., 0., 0., 0., 24., 186., 118.3, 387.3}; Show[ ListPlot[{{0.5, -250}, {4.5, 800}}, PlotRange -> {{0.5, 4.5}, {-250, 800}}, Frame -> True, FrameTicks -> {{Automatic, Automatic}, {{{1.5, "Jan"}, {3.5, "Feb"}}, None}}, PlotStyle -> White, Frame -> True], BoxWhiskerChart[{{}, Jan, {}, Feb}], DistributionChart[{Jan, {}, Feb, {}}, ChartElementFunction -> "SmoothDensity"], DistributionChart[{Jan, {}, Feb, {}}, ChartElementFunction -> "PointDensity", ChartStyle -> Directive[{GrayLevel[10, 10], Opacity[0.3], EdgeForm[]}]] ] But your data is problematic for the available density plot in `DistributionChart` because those distributions are (likely) bounded by zero. Getting an appropriate density function for such cases would require the `"Bounded"` option in `SmoothKernelDistribution`.

Here's a very ad hoc approach:

Jan = {2.09, 0.9, 317.4, 472.400, 417.79, 234.200, 325., 524.2, 49.59,
    114.7, 126.1, 136., 160.6, 203.2, 157.8, 0., 8., 23.5};

Feb = {0., 0., 0.5, 111.2, 155.700, 324.59, 152.5, 348.3, 222., 0., 
   0., 0., 0., 0., 24., 186., 118.3, 387.3};

Show[
 ListPlot[{{0.5, -250}, {4.5, 800}}, PlotRange -> {{0.5, 4.5}, {-250, 800}}, Frame -> True,
  FrameTicks -> {{Automatic, Automatic}, {{{1.5, "Jan"}, {3.5, "Feb"}}, None}}, PlotStyle -> White, Frame -> True],
 BoxWhiskerChart[{{}, Jan, {}, Feb}],
 DistributionChart[{Jan, {}, Feb, {}}, ChartElementFunction -> "SmoothDensity"],
 DistributionChart[{Jan, {}, Feb, {}}, ChartElementFunction -> "PointDensity", 
  ChartStyle -> Directive[{GrayLevel[10, 10], Opacity[0.3], EdgeForm[]}]]
 ]

Density and box plots

But your data is problematic for the available density plot in DistributionChart because those distributions are (likely) bounded by zero. Getting an appropriate density function for such cases would require the "Bounded" option in SmoothKernelDistribution.