Question
Hello, How can I generate a uniformly distributed random vector with its sum to be equal to 1?
Expert Answer
Prashant Kumar
PhD Expert
Answered Aug 14, 2026
Too many people think that generating a uniform sample, then normalizing by the sum will generate a uniform sample. In fact, this is NOT at all true.
A good way to visualize this is to generate that sample for the 2-d case. For example, suppose we do it the wrong way first?
xy = rand(100,2); plot(xy(:,1),xy(:,2),'.')
Now, lets do the sum projection that virtually everyone poses. (Yes, it is the obvious choice. Now we will see why it is the wrong approach.)
xys = bsxfun(@rdivide,xy,sum(xy,2)); hold on plot(xys(:,1),xys(:,2),'ro') axis equal axis square
The sum-projected points lie along the diagonal line. Note the distribution seems to be biased towards the middle of the line. A uniform sample would have points uniformly distributed along that line.
In a low number of dimensions there are some nice tricks to generate a sample that is indeed uniform. I tend to use Roger Stafford's submission to the file exchange, randfixedsum. It is efficient, and works in any number of dimensions.
figure xyr = randfixedsum(2,100,1,0,1)'; plot(xyr(:,1),xyr(:,2),'ro') axis equal axis square
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