Editor's Note: This file was selected as MATLAB Central Pick of the Week
The zipfile contains the following files for visualizing distributions:
 distributionPlot.m: main function that allows creating violin plots
 myHistogram.m: generate histograms with 'ideal' bin width given the number of data points and the spread (FreedmanDiaconis rule). Note that for integervalued data, each integer gets its own bin.
In addition, the zip file contains four helper functions: countEntries, colorCode2rgb, isEven, myErrorbar
If you want to overlay individual data points, you need to download the separate submission plotSpread (http://www.mathworks.com/matlabcentral/fileexchange/37105).
DistributionPlot allows visualizing multiple distributions side by side. It is useful for skewed unimodal data and indispensable for multimodal data. DistributionPlot is especially useful for showing the time evolution of a distribution.
Some of the examples from the help:
r = rand(1000,1);
rn = randn(1000,1)*0.38+0.5;
rn2 = [randn(500,1)*0.1+0.27;randn(500,1)*0.1+0.73];
rn2=min(rn2,1);rn2=max(rn2,0);
figure
ah(1)=subplot(2,4,1:2);
boxplot([r,rn,rn2])
ah(2)=subplot(2,4,3:4);
distributionPlot([r,rn,rn2],'histOpt',2); % histOpt=2 works better for uniform distributions than the default
set(ah,'ylim',[1 2])
%additional options
data = [randn(100,1);randn(50,1)+4;randn(25,1)+8];
subplot(2,4,5)
distributionPlot(data); % defaults
subplot(2,4,6)
distributionPlot(data,'colormap',copper,'showMM',5,'variableWidth',false) % show density via custom colormap only, show mean/std,
subplot(2,4,7:8)
distributionPlot({data(1:5:end),repmat(data,2,1)},'addSpread',true,'showMM',false,'histOpt',2) %autobinwidth depends on # of datapoints; for small n, plotting the data is useful
Jonas (2020). Violin Plots for plotting multiple distributions (distributionPlot.m) (https://www.mathworks.com/matlabcentral/fileexchange/23661violinplotsforplottingmultipledistributionsdistributionplotm), MATLAB Central File Exchange. Retrieved .
1.15.0.0  renamed histogram to myHistogram to avoid clash with new Matlab function of the same name, added support for boxplot overlays 

1.14.0.0  Improved documentation (more examples, link to plotSpread), added quantiles (thanks to Warwick for suggestion & testing). Also, belated thanks to Kelly for suggesting horizontal orientation. 

1.13.0.0  Added the following new features:
Additionally, plotSpread is now a separate submission. 

1.12.0.0  Added option to align the bars at the left or the right (option "histOri"), as suggested by Yuri. Also, bugfix. 

1.9.0.0  Improved normalization options. Thanks to Jake for the suggestion. 

1.7.0.0  Fixed a bug in the code, and two mistakes in the example. 

1.6.0.0  Made colorbar more meaningful if there is only one colormap and the bins are normalized globally (i.e. globalNorm is set to 1). Thanks to Brian Katz for the suggestion. 

1.4.0.0  Changed input from optional arguments to parameterName/parameterValue pairs (note that the old syntax still works!).


1.3.0.0  Updated title to Violin Plot, because that's how (part) of these plots are called elsewhere. 

1.2.0.0  Documented previously undocumented functionality, chose better screenshot to demonstrate how distributionPlot is better for comparing distributions than boxplot 

1.1.0.0  Fixed cryptic error if the data was all NaNs (thanks Christopher for pointing it out!).

Create scripts with code, output, and formatted text in a single executable document.
Excellent tool, are you willing to add style options as suggested in https://rupress.org/jcb/article/219/6/e202001064/151717/SuperPlotsCommunicatingreproducibilityand?
Such as:
 Violin with only borders
 Spread point collor according to 2nd order dim
 Mean of subpopulation (2nd order) with corresponding color and style
good variety of plot options
Works well. The examples are very helpful. Plotting different distributions on the left and right of a single violin was unclear at first, but the example in the comments made it clear that the widthDiv parameter is necessary here. Perhaps a bit more description on this feature would be helpful. My only minor issue with this plotting tool is the limited aesthetics ability of the plots for adjusting edge and face color and transparency.
To add to the previous comment I am looking for split violin plots.
Nice submission. I am new to violin plots. I have a plot I would like to generate. I have results from pre and post contrast agent I would like to use a single violin plot to show them i.e left side of the single plot pre and right side of the plot post agent. Does your script allow for such plots?
Thank you for the tool. I am new to this. Can anybody help me know, where to give my input for xvalues and yvalues.
Great submission! Thanks. One question though: is there any way to control the bin width so that different distributions have equal widths?
I just realised that the function 'histogram' was renamed for download (but not in the function tab above). So everything is fine.
Thanks for sharing!
Did you thought about renaming your function 'histogram(varargin)'? It might shadow MATLAB's function 'histogram' Introduced in R2014b, which requires different input. This might cause confusion.
Whoops, I didn't mean to post that last comment...please ignore.
There appears to be a sizable bug when using strings (matrices or cell arrays) as categories. The data ignore the order of the categories, leading to arbitrary data distributions. Here's an example. Results are bad when the categories are 'a' and 'b', results are fine if the categories are 1 and 2.
a=randn(1000,1)+(1:1000).';
b=[repmat('a',500,1);repmat('b',500,1)];
% b=[repmat(1,500,1);repmat(2,500,1)];
figure
distributionPlot(a,'histOpt',0,'addspread',1,'groups',b,'showMM',6)
figure
distributionPlot(a,'histOpt',0,'addspread',1,'groups',flipud(b),'showMM',6)
Thanks for posting! This is a great tool.
One quick fix suggsted: when plotting using xValues option, should to modify line 905 using unique() as follows:
set(ah,'XTick',unique(sortedX));
else function will throw an error when there are repeat x values:
Error using matlab.graphics.axis.Axes/set
Value must be a vector of type single or double whose values increase
Hi there, as I'm new to matlab, can someone advise on how and where should I input my data? Thanks.
wj
Thanks for the code!
I found an error when wanting to use legends with distributionPlot.m. The first output handles (patch) return an integer instead of a Patch (CS). To fix it is quite simple:
line 44: hh = {}; % Instead of NaN(nData,1);
line 729: hh{iData} =...
line 731: hh{iData} =...
I don't know if there is place to suggest changes in Matlab File Exchange. I hope the author or somebody else can do this fix.
Thanks for the submission.
How can i add a legend using widthDiv to compare two series of distributions ?
using : legend('1','2') give me two blue box.
thx again
Great, Great, Great! Congrats Jonas!
One little suggestion: it would be amazing being able to constrain the density estimation within a given interval, so not to obtain "undesired tails" that trespass the desired lower and upper bound values  for example if you are plotting the violin plot from a set of scores that can only range from, say, 1 to 100, in order to prevent the tails of the violin spanning from values smaller than 1 and larger than 100.
This is a great tool thank you. Is there an option to make the distribution plot higher in resolution? It looks pixelated.
I get around this by editing the ksdensity function call at 603. ksdensity takes a 'pts' argument where you can specify an arbitrary number of points to get finer resolution violin plots.
Great peace of code, just I was looking for. However, I have a question: Is there any way to normalize histograms across comparison (i.e. when using the option "widthDiv") such that both the left and right distributions will have the same area?
Sorry, this was my mistake in a way. If the data vector is a row, not a column, the result of the grouping are identical datasets. Could be good to put a check in here, to verify that the dimensions of the data and the grouping variable are the same.
Can anyone confirm that this works with grouping the variable (and under which MatLab version)? I am having problems. Maybe an example would be good to confirm this. I get identical group data after grouping (R2017a).
@Wynn, Markus: I have updated distributionPlot and renamed histogram.m
I'd like to echo Markus Millinger's comment that the code overwrites the MATLAB builtin 'histogram' function. Any chance of a patch with a renamed 'histogram.m'?
Great, Thanks, very useful!
Is there an option to use the addSpread function and color the dots using different values so adding another dimension to the data?
This is great, thanks. However, would you consider adding an option to cut plots off in the ydirection at the min and max of the dataset?
This is very nice! However, the function histogram clashes with the "new" Matlab function with the same name.
Neat and nice. Much better than the boxplot for scientific work
Displaying distributional differences provide more information of the samples and are very useful when distance from zero is meaningless.
Furthermore, the option to overlay the mean, SEM, sd and percentiles helps us better interpret the statistical analyses.
Overall, an invaluable option to the classic barplots and boxplots.
Excellent, just what I needed. It served me very well.
I added a modified version to the MatLabFEx using the smooth kernel density (Violin Plot based on kernel density estimation).
@Warwick: this looks like a bug  globalNorm=2 should do the trick, but at the moment, it seems like it would require equally spaced bins. I'll look into it.
This is a great function. However I want to discriminate between two quite different distributions. I have a problem getting the Total area under the respective curves to be equal (to a nominal 1) for separate datasets (even with the same number of observations). Eg, Say I want to plot U and V left and right respectively where
U = normrnd(3.3,1.0,100,1);
V = normrnd(2.0,0.3,100,1);
then no matter what I do, they don't look anywhere near equal. Any ideas? or have I missed something obvious?
This is a great tool... It would be nice if some of the functionality could be achieved without requiring toolboxes (e.g. I've cobbled together the code to do the smoothed histograms without the spline toolbox, using files from FEX).
@all: thanks again for the suggestions, most of which are implemented now. Please note that plotSpread is now a submission on its own that needs to be downloaded separately.
Very, very useful!
@Yuri Kotliarov: I suggest you call addSpread.m directly, rather than via distributionPlot.m
@all: thanks for the good suggestions. I hope I can implement them soon!
@Jonas, I didn't find if there is a way to change the width of dots spread (addSpread is 1). It doesn't seem to depend on distWidth. If I don't show the density (color is white), the distance between groups is quite large. Thanks.
Overall, this is a great function, and I use it quite often to analyze model ensemble output. A few enhancements that could be nice:
 Add the option to display in a horizontal orientation.
 Add the option to filter outliers when calculating bin widths and kernal densities. Could also be nice to display these as points, as in boxplot, rather than connecting them via long lines to the main histogram.
 This is an edge case, but the function will error under the addSpread option if a column/group contains only NaNs and/or Infs.
This is very good. I've just included some plots in a report. Thank you. Possibly you could add an extra feature within the options of 'showMM' = 6, say, which would be to draw a horizontal line of linewidth 2 for the median, and 25 & 75 pctiles at linewidth 1.
@Yuri: I have implemented your suggestion (though I start the histograms from the very left or right side, respectively), and fixed the previous bug.
@Jonas: Thanks for the answer. May I suggest a new feature? It would be nice to draw histogram at certain direction. Currently it's only centered, but also can be left or right directed. All you need to change is xBase variable at line 401: 0.5 to 0 for left direction, 0.5 to 0 for right direction. For someone it's easier to understand when the distributions looks like turned histograms.
@Yuri Kotliarov: Currently, the only workaround is to call ksdensity outside of distributionPlot to ensure that the smoothing uses the same kernel:
x = zeros(10,1);
y = x+randn(10,1)*0.1;
[yy(:,2),yy(:,1)] = ksdensity(y,'width',0.01);
[xx(:,2),xx(:,1)] = ksdensity(x,'width',0.01);
distributionPlot({xx,yy},'showMM',false)
Unfortunately, the showMM option is bugged when you supply your own histograms at the moment, so you have to set that option to false.
@Jonas: I have problem with smoothing (histOpt=1) when all values for a group are the same. In this case the distribution plot is very wide comparing to the same data with a little variance.
For example:
x = zeros(10,1);
y = x+randn(10,1)*0.1;
distributionPlot({x,y},'histOpt',1,'addSpread',1)
The same happens with a few outliers in x. I understand it's probably how ksdensity function works. But can you do anything to make the above cases comparable?
@Yuri: The new version of distributionPlot supports grouped data.
Great! Thanks.
@Yuri: No, it doesn't work with grouped data (yet). In the meantime, you can use a function like group2cell (http://www.mathworks.com/matlabcentral/fileexchange/11192group2cell) to distribute your grouped data among cells to use with distributionPlot.
@Brian: Thanks for the suggestions, and for sending me your sample code. I have not had time yet to update my code, though, but I will look into it!
Does it work with grouped data, like boxplot does?
This works quite well, giving a very interesting data presentation method. Some improvements could be the use of a colormap, rather than a fored gray scale. An example in teh help would also be a good addition.
I have started to try and make a combined plot which allows for both boxplot (using boxplotCsub) and distributionPlot. As both are symetrical, they can both be collapsed to onesided and then combing, giving two very interesting looks at the same data sets.
Very very cool.