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

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?

Answer 1

[the cyclist]

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.

[Amr Hashem]

I used this code to change color for each:

 hist(H,34)
 h = findobj(gca,'Type','patch');
set(h,'FaceColor','b','EdgeColor','w')

but it changed all by the last color

[Image Analyst]

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.

Answer 2

[Image Analyst]

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.
mask = counts1>0 & counts2>0;
% Sum both histograms in that area.
sum1 = sum(counts1(mask)) + sum(counts2(mask))

% Get indexes of second overlap region.
mask = counts2>0 & counts3>0;
% Sum both histograms in that area.
sum2 = sum(counts2(mask)) + sum(counts3(mask))

% Get indexes of third overlap region.
mask = counts3>0 & counts4>0;
% Sum both histograms in that area.
sum3 = sum(counts3(mask)) + sum(counts4(mask))

% Get indexes of fourth overlap region.
mask = counts4>0 & counts5>0;
% Sum both histograms in that area.
sum4 = sum(counts4(mask)) + sum(counts5(mask))

[Amr Hashem]

it gives me the values of overlaped regions but nothing change in the figure (didn't plot them on the graph )

[Image Analyst]

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);