How do I merge a boxplot with distribution plot?

Questions
,
1

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 -> {{"\!\(\*
StyleBox[\"Jan\",\nFontSize->16]\)", "\!\(\*
StyleBox[\"Feb\",\nFontSize->16]\)"}}]

thumbnail.jpg
thumbnail.jpg446×378 23.3 KB

2

You may try with Epilog and Inset.

3

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[]}]]
 ]

boxplots.png
boxplots.png960×608 24.3 KB

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.

4

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

5

Thank you so much, Jim.
I appreciate your time.