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Boxplot and histogram in one plot

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Jakob Seifert
Jakob Seifert on 6 May 2021
Commented: RJ on 31 Jul 2021
Hey,
I think this question has been asked before:
But I could not find any proper solution;
so is there a way to achieve something like this:
I'm looking forward to hear your suggestions :)
  1 Comment
Sambit Supriya Dash
Sambit Supriya Dash on 6 May 2021
Yes it is possible to get boxplot and histogram in one plot,
Example,
x = [1 2 3;4 5 6;7 8 9];
y = [5 4 3; 5 7 9; 1 9 3];
figure(1)
hist(x)
hold on
boxplot(y)
hold off
Hope, it helps.

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Accepted Answer

Adam Danz
Adam Danz on 7 May 2021
Edited: Adam Danz on 7 May 2021
This method uses patch objects to display histograms next to each boxplot. It's based on another answer that displays probability density distributions next to vertical scatter plots.
You only need to replace the x and y data and can copy-paste the rest of the code.
Inputs.
x : 1xn vector defining the x coordinate of n boxplots.
y : mxn matrix of raw data for n boxplots
rng('default') % for reproducibility
x = 0:5:30;
y = (randn(300, numel(x)) + linspace(.5,5,numel(x))) .* linspace(.5,2,numel(x));
Set spacing
binWidth = 0.4; % histogram bin widths
hgapGrp = .05; % horizontal gap between pairs of boxplot/histograms (normalized)
hgap = 0.2; % horizontal gap between boxplot and hist (normalized)
Compute histogram counts & edges
hcounts is an nx2 cell array containing the {counts, edges} for each distribution.
maxCount is the maximum bin count across all distributionts, used to normalize patch heights
hcounts = cell(size(y,2),2);
for i = 1:size(y,2)
[hcounts{i,1}, hcounts{i,2}] = histcounts(y(:,i),'BinWidth',binWidth);
end
maxCount = max([hcounts{:,1}]);
Plot boxplots
fig = figure();
ax = axes(fig);
hold(ax,'on')
xInterval = mean(diff(sort(x))); % x-interval (best if x is at a fixed interval)
normwidth = (1-hgapGrp-hgap)/2;
boxplotWidth = xInterval*normwidth;
boxplot(ax,y,'Positions',x,'Widths',boxplotWidth,'OutlierSize',3,'Labels',compose('%d',x))
Add vertical histograms (patches)
histX0 = x + boxplotWidth/2 + hgap; % histogram base
maxHeight = xInterval*normwidth; % max histogram height
patchHandles = gobjects(1,size(y,2));
for i = 1:size(y,2)
% Normalize heights
height = hcounts{i,1}/maxCount*maxHeight;
% Compute x and y coordinates
xm = [zeros(1,numel(height)); repelem(height,2,1); zeros(2,numel(height))] + histX0(i);
yidx = [0 0 1 1 0]' + (1:numel(height));
ym = hcounts{i,2}(yidx);
% Plot patches
patchHandles(i) = patch(xm(:),ym(:),[0 .75 1],'FaceAlpha',.4);
end
xlim([-2.5, 32.5])
Method 2 with color control
With just a few changes to the code above, you can use boxplotGroup() from the file exchange to set up colors of boxplots and histogram similar to the example in your question.
%% Inputs
rng('default') % for reproducibility
x = 0:5:30;
y = (randn(300, numel(x)) + linspace(.5,5,numel(x))) .* linspace(.5,2,numel(x));
%% Set Spacing
binWidth = 0.4; % histogram bin widths
hgapGrp = .15; % horizontal gap between pairs of boxplot/histograms (normalized)
hgap = 0.06; % horizontal gap between boxplot and hist (normalized)
%% Compute histogram counts & edges
hcounts = cell(size(y,2),2);
for i = 1:size(y,2)
[hcounts{i,1}, hcounts{i,2}] = histcounts(y(:,i),'BinWidth',binWidth);
end
maxCount = max([hcounts{:,1}]);
%% Plot boxplotsGroup()
fig = figure();
ax = axes(fig);
hold(ax,'on')
% Convert y (mxn matrix) to 1xn cell array of mx1 vectors, required by boxplotWidths
yc = mat2cell(y,size(y,1),ones(1,size(y,2)));
xInterval = 1; %x-interval is always 1 with boxplot groups
normwidth = (1-hgapGrp-hgap)/2;
boxplotWidth = xInterval*normwidth;
% Define colors for each boxplot
colors = lines(size(y,2));
% Plot colored boxplots
bph = boxplotGroup(ax,yc,'Widths',boxplotWidth,'OutlierSize',3,'PrimaryLabels',compose('%d',x),'Colors',colors);
set(findobj(bph.boxplotGroup,'-property','LineWidth'), 'LineWidth', 1) % increase line widths
%% Add vertical histograms (patches) with matching colors
xCoordinate = 1:size(y,2); %x-positions is always 1:n with boxplot groups
histX0 = xCoordinate + boxplotWidth/2 + hgap; % histogram base
maxHeight = xInterval*normwidth; % max histogram height
patchHandles = gobjects(1,size(y,2));
for i = 1:size(y,2)
% Normalize heights
height = hcounts{i,1}/maxCount*maxHeight;
% Compute x and y coordinates
xm = [zeros(1,numel(height)); repelem(height,2,1); zeros(2,numel(height))] + histX0(i);
yidx = [0 0 1 1 0]' + (1:numel(height));
ym = hcounts{i,2}(yidx);
% Plot patches
patchHandles(i) = patch(xm(:),ym(:),colors(i,:),'EdgeColor',colors(i,:),'LineWidth',1,'FaceAlpha',.45);
end
  5 Comments
RJ
RJ on 31 Jul 2021
Awesome thanks, I got it working with padcat.

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More Answers (1)

Scott MacKenzie
Scott MacKenzie on 6 May 2021
Edited: Scott MacKenzie on 7 May 2021
This solution uses tiledlayout and boxchart, but you can adjust to use subplot and boxplot if you are running an older version of MATLAB:
n = 7;
y = randn(100,n);
tiledlayout(1, 2*n);
for i=1:n
nexttile;
boxchart(y(:,i));
set(gca,'visible', 'off', 'ylim', [-4 4]);
nexttile;
histogram(y(:,i), 20, 'orientation', 'horizontal');
set(gca,'visible', 'off', 'ylim', [-4 4]);
end
f = gcf;
f.Color = 'w';
f.Units = 'normalized';
f.Position = [.1 .2 .8 .4];
  6 Comments
Scott MacKenzie
Scott MacKenzie on 7 May 2021
Hey, good point. Thanks. I just adjusted my solution to prevent this -- by setting the y-axis limits.

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