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### Highlights from Violin Plots for plotting multiple distributions (distributionPlot.m)

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# Violin Plots for plotting multiple distributions (distributionPlot.m)

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13 Apr 2009 (Updated )

Function for plotting multiple histograms side-by-side in 2D - better than boxplot.

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

File Information
Description

The zip-file contains the following files for visualizing distributions:

- distributionPlot.m: main function that allows creating violin plots

- histogram.m: generate histograms with 'ideal' bin width given the number of data points and the spread (Freedman-Diaconis rule). Note that for integer-valued 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])
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) %auto-binwidth depends on # of datapoints; for small n, plotting the data is useful

Acknowledgements

Plot Spread Points (Beeswarm Plot) inspired this file.

This file inspired Violin Plot Based On Kernel Density Estimation.

MATLAB release MATLAB 7.6 (R2008a)
Other requirements The 'smooth' option of histogram.m requires the spline toolbox. However, for smooth histograms ksdensity is probably the better choice, anyway. Grouped data requires the statistics toolbox.
21 Jan 2014

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).

17 Mar 2013

@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.

17 Mar 2013

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?

04 Oct 2012
15 Jun 2012

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).

14 Jun 2012

@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.

13 Apr 2012

Very, very useful!

19 Mar 2012

@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!

19 Mar 2012

@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.

19 Mar 2012

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.

01 Mar 2012

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.

14 Dec 2011

@Yuri: I have implemented your suggestion (though I start the histograms from the very left or right side, respectively), and fixed the previous bug.

16 Nov 2011

@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.

01 Nov 2011

@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.

31 Oct 2011

@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;

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?

07 Jul 2011
21 Jun 2011

@Yuri: The new version of distributionPlot supports grouped data.

24 Jan 2011

Great! Thanks.

20 Jan 2011

@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/11192-group2cell) to distribute your grouped data among cells to use with distributionPlot.

20 Jan 2011

@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!

15 Dec 2010

Does it work with grouped data, like boxplot does?

23 Sep 2010

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 one-sided and then combing, giving two very interesting looks at the same data sets.

28 Aug 2010

Very very cool.

21 Jul 2010
12 May 2010
11 May 2010
21 Nov 2009
09 Sep 2009
25 Jun 2009
28 Apr 2009
19 Apr 2009
16 Apr 2009

Fixed cryptic error if the data was all NaNs (thanks Christopher for pointing it out!).
distributionPlot now also automatically converts arrays in cells to vectors and throws a warning.

25 Apr 2009

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

20 Jan 2011

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

20 Jun 2011

Changed input from optional arguments to parameterName/parameterValue pairs (note that the old syntax still works!).
Added several new features, such as support for grouped variables, overlay of data points, and user-defined colormaps.

20 Jun 2011

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.

21 Jun 2011

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

02 Oct 2011

Improved normalization options. Thanks to Jake for the suggestion.

14 Dec 2011

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

12 Jun 2012