MATLAB: how can I generate 2 random numbers which sum is less than 1?

Question

Does anybody know how to generate two random numbers which sum is less than one?

I found only topics describing how to generate 2 random numbers which add up to 1 (trough normalization)

The obvious solution would be to normalize them to anything less than one. Do you want to achieve a certain distribution or do you want your numbers to have certain properties? — Dennis Jaheruddin, Jan 23 '14 at 11:04
I see now that the condition is "sum _less than_", not "sum _equal to_". So I'm retracting my duplicate-question vote — Luis Mendo, Jan 23 '14 at 11:45

score 2 · Accepted Answer · answered Jan 23 '14 at 11:02

2

answered Jan 23 '14 at 11:02

normKrumpe

I suppose you would need to generate sum first, and then make sure r1 is generated less than sum. (Or generate sum to be larger than r1) otherwise you could have `r1=0.8, sum=0.4, r3=-0.4` which I expect to be undesirable. – Dennis Jaheruddin Jan 23 '14 at 11:07
I wondered that too, but original post put no bounds on the two numbers...only on their sum. – normKrumpe Jan 23 '14 at 11:09
Your answer is indeed correct, but in this case I would recommend you to mention the assumption that negative numbers are allowed. That may help the asker even more! – Dennis Jaheruddin Jan 23 '14 at 11:14
Sorry if I bother you again... How I can do if I want to generate a third variable which squared value is less than the product of the first two variables? In practice what I'm trying to do is to generate a positive-definite 2x2 matrix... – Alessandro Beretta Jan 23 '14 at 12:00

score 1 · Answer 2 · answered Jan 23 '14 at 10:59

1

Assuming you don't care too much about the distribution:

x = rand(2,1);
if sum(x)>1
   x=x/2;
end

answered Jan 23 '14 at 10:59

Dennis Jaheruddin

score 0 · Answer 3 · edited May 23 '17 at 10:31

0

Modifying normKrumpe's answer, I'd suggest

edited May 23 '17 at 10:31

Community

answered Jan 23 '14 at 11:26

glglgl

3 Answers3