# how to sum a group of gaussian distribution using "hist" ?

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Amr Hashem on 4 Nov 2015
Commented: Image Analyst on 5 Nov 2015
I want to add five gaussian distributions at different points on x-axis
I try:
n=500;
H1 = normrnd(14,5,n,1); % generate random numbers of normal distribution at mu and sigma
H2 = 24+ normrnd(14,5,n,1); % start from 24
H3 = 48+ normrnd(14,5,n,1);
H4 = 72+ normrnd(14,5,n,1);
H5 = 96+ normrnd(14,5,n,1);
figure
hhh = [H1 H2 H3 H4 H5];
hist(hhh,130)
which produce a good figure as I need: but I want to plot the total values of the intersected area. (I put a circle on them)
How I can sum them?

the cyclist on 4 Nov 2015
Edited: the cyclist on 4 Nov 2015
One simple possibility is to create one 2500x1 vector of the data rather than the 550x5 array you have, which is as simple as
hhh = [H1; H2; H3; H4; H5];
in place of
hhh = [H1 H2 H3 H4 H5];
If you do that, you will lose the distinct colors of the five histograms. But if you don't do it that way, you will have the problem of coloring the summed histograms, which gets tricky.
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Image Analyst on 5 Nov 2015
But with this method, you don't know which bins are in the "overlap/intersection" region and which are not. Determining "total values of the intersected area" was a requirement/request.

Image Analyst on 4 Nov 2015
Try it like this, to sum the bins where both histograms are non-zero:
n=500;
H1 = normrnd(14,5,n,1); % generate random numbers of normal distribution at mu and sigma
H2 = 24+ normrnd(14,5,n,1); % start from 24
H3 = 48+ normrnd(14,5,n,1);
H4 = 72+ normrnd(14,5,n,1);
H5 = 96+ normrnd(14,5,n,1);
figure
hhh = [H1 H2 H3 H4 H5];
hist(hhh,130)
edges = -20:140;
counts1 = histc(H1, edges);
counts2 = histc(H2, edges)
counts3 = histc(H3, edges);
counts4 = histc(H4, edges);
counts5 = histc(H5, edges);
% Get indexes of first overlap region.
% Sum both histograms in that area.
% Get indexes of second overlap region.
% Sum both histograms in that area.
% Get indexes of third overlap region.
% Sum both histograms in that area.
% Get indexes of fourth overlap region.
% Sum both histograms in that area.
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Image Analyst on 5 Nov 2015
I thought you could just use text() if you wanted some label on there, like
message = sprintf('The sum here = %d', sum1);
text(x,y,message);