Normalize a histogram to a different datasets, Normalize two histograms to their sum

Hi everyone,

i want to plot two datasets on the same histogram, however one group of the dataset represent cars going fast and the other group represent the slow ones, i want to plot both of them on the same histogram, but when i normalize it, it uses the number of observations for each group (e.g. if i have 100 fast cars and 15 slow cars it will be normalized (divided) according to 100 & 15), but i want both groups to be normalized to their sum = 115 vehicles so that the slow cars will appear in a tiny bars next to the fast ones. you can see the figure to make it more clear.

can anyone help me with that please?

thanks,

[Luna]

Share the code with the data please so we can look at it.

[MJ]

% find any vehicles that speed is less than 1 mph
NBL2SLOW = NBL2 (ismember ((NBL2 (:,12) <1), 1),:);
% take the unique ID of them to separate them
uniqueNBL2SLOW = unique (NBL2SLOW (:,1));
NBL2s = NBL2 (ismember (NBL2(:,1), uniqueNBL2SLOW),:);
NBL2f = NBL2 (~ismember (NBL2(:,1), uniqueNBL2SLOW),:);

% create an index for each individual car ID, 1 is column number
[NBL2sid,~,NBL2sindex] = unique (NBL2s (:,1));
%find max and min of travel stamp for each unique car ID
NBL2smaxtt = accumarray (NBL2sindex, NBL2s (:, 4),[],@max );
NBL2smintt = accumarray (NBL2sindex, NBL2s (:, 4),[],@min );
% create a summary table
NBL2ssummary = [NBL2sid NBL2smaxtt NBL2smintt];
% find travel time and convert to seconds
NBL2ssummary (:,4) = (NBL2ssummary (:,2) - NBL2ssummary (:,3))/77.65151515;

% create an index for each individual car ID, 1 is column number
[NBL2fid,~,NBL2findex] = unique (NBL2f (:,1));
%find max and min of travel stamp for each unique car ID
NBL2fmaxtt = accumarray (NBL2findex, NBL2f (:, 4),[],@max );
NBL2fmintt = accumarray (NBL2findex, NBL2f (:, 4),[],@min );
% create a summary table
NBL2fsummary = [NBL2fid NBL2fmaxtt NBL2fmintt];
% find travel time and convert to seconds
NBL2fsummary (:,4) = (NBL2fsummary (:,2) - NBL2fsummary (:,3))/77.65151515;

% plot both NBL2fsummary & NBL2ssummary of the same graph
NBL2fhistogram = histogram (NBL2fsummary (:,4),'BinWidth',10,'Normalization','probability');
hold on
NBL2shistogram = histogram (NBL2ssummary (:,4),'BinWidth',10,'Normalization','probability','faceColor', 'r', 'FaceAlpha',.2);
title ('Link 2 NB');
legend ('Vehicles Did not Stop','Vehicles Stopped');
xlabel ('Travel Rate (Sec/mi)');
ylabel ('Relative Frequency (%)');
xlim ([0, inf]);
xtickangle (90);
yticklabels (yticks*100);
hold off

as you can see:

NBL2fhistogram = histogram (NBL2fsummary (:,4),'BinWidth',10,'Normalization','probability');
NBL2shistogram = histogram (NBL2ssummary (:,4),'BinWidth',10,'Normalization','probability','faceColor', 'r', 'FaceAlpha',.2);

they both are normalized based on their individual counts, but in reality i want to show that the slow vehicles are less than the fast ones, which will make their distribution shorter.

[Adam Danz]

Instead of normalizing by dividing by 100 & 15, why not just divide by 115?

[MJ]

I don't divide it manually by anything, i am telling how MATLAB does it, i am -in fact- looking for a way to divide by 115 (a user defined number let's say).

Answer 1

[Adam Danz]

Idea 1

This is a little bit of a hack but you could add NaN values to each histogram input so that it has 115 elements. Then the probability normalization will normalize by n=115 rather than the number of non-nan datapoints. That would look something like this.

data = nan(1,115); 
data(1:length(NBL2fsummary(:,4))) = NBL2fsummary(:,4); 
NBL2fhistogram = histogram (data,'BinWidth',10,'Normalization','probability');

Idea 2

Use histcounts() and bar() instead of histogram() and normalize the data yourself. Pro: you're doing the normalization instead of using a black box. Con: you lose a lot of nice features that come with histogram().

It would look something like this:

n = histcounts(NBL2fsummary(:,4), edges);           %you create the edges
m = histcounts(NBL2ssummary(:,4), edges); 
count = sum([n,m]);                            %number of data points (used in normalization)
b2 = bar(edges(1:end-1), n/count, 'histc');    % n/count is the normalization

[MJ]

Perfect, the first idea woked well.

thank you very much. this was my data before,

and this is how it looks now (the correct way).

and this is the modified code:

% find any vehicles that speed is less than 1 mph
% the 1 after the comma here is logical and means is true, 0 means false
NBL1SLOW = NBL1 (ismember ((NBL1 (:,12) <1), 1),:);
% take the unique ID of them to separate them
uniqueNBL1SLOW = unique (NBL1SLOW (:,1));
NBL1s = NBL1 (ismember (NBL1(:,1), uniqueNBL1SLOW),:);
NBL1f = NBL1 (~ismember (NBL1(:,1), uniqueNBL1SLOW),:);

% create an index for each individual car ID, 1 is column number
[NBL1sid,~,NBL1sindex] = unique (NBL1s (:,1));
%find max and min of travel stamp for each unique car ID
NBL1smaxtt = accumarray (NBL1sindex, NBL1s (:, 4),[],@max );
NBL1smintt = accumarray (NBL1sindex, NBL1s (:, 4),[],@min );
% create a summary table
NBL1ssummary = [NBL1sid NBL1smaxtt NBL1smintt];
% find travel time and convert to seconds
NBL1ssummary (:,4) = (NBL1ssummary (:,2) - NBL1ssummary (:,3))/NBL1length;
% create fake cells to fill the slow and fast vehicles to the number of total vehicles
NBL1sdata = nan(1,length (NBL1id));
NBL1sdata(1:length(NBL1ssummary(:,4))) = NBL1ssummary(:,4);
% create the histogram
NBL1shistogram = histogram (NBL1sdata,'BinWidth',10,'Normalization','probability');


% create an index for each individual car ID, 1 is column number
[NBL1fid,~,NBL1findex] = unique (NBL1f (:,1));
%find max and min of travel stamp for each unique car ID
NBL1fmaxtt = accumarray (NBL1findex, NBL1f (:, 4),[],@max );
NBL1fmintt = accumarray (NBL1findex, NBL1f (:, 4),[],@min );
% create a summary table
NBL1fsummary = [NBL1fid NBL1fmaxtt NBL1fmintt];
% find travel time and convert to seconds
NBL1fsummary (:,4) = (NBL1fsummary (:,2) - NBL1fsummary (:,3))/NBL1length;
% create fake cells to fill the slow and fast vehicles to the number of total vehicles
NBL1fdata = nan(1,length (NBL1id));
NBL1fdata(1:length(NBL1fsummary(:,4))) = NBL1fsummary(:,4);
% create the histogram
NBL1fhistogram = histogram (NBL1fdata,'BinWidth',10,'Normalization','probability');

NBL1fhistogram = histogram (NBL1fdata,'BinWidth',10,'Normalization','probability');
hold on
NBL1shistogram = histogram (NBL1sdata,'BinWidth',10,'Normalization','probability','faceColor', 'r', 'FaceAlpha',.2);
title ('Link 1 NB');
legend ('Vehicles Did not Stop','Vehicles Stopped');
xlabel ('Travel Rate (Sec/mi)');
ylabel ('Relative Frequency (%)');
xlim ([0, inf]);
%xticks (0:100:10000);
%yticks (0:.02:1);
xtickangle (90);
yticklabels (yticks*100);
hold off

again, thank you

[Adam Danz]

Nice work! I didn't look through the code but if you have any other questions I'd be glad to help.

[MJ]

thank you very much, i appreciate it