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

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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?

##### 0 Comments

### Accepted Answer

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.

##### 2 Comments

Image Analyst
on 5 Nov 2015

### More Answers (1)

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.

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))

##### 2 Comments

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);

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