How to generate multiple Vectors with random variables but sum 1

Hello Folks, i want to create multiple Vectors with random variables (btw. 0 and 1) but sum 1

for example [0 1 0 0] or [0.7 0.2 0 0.1] and so on

i want to scatterplot a large number of random portfolios and therefore i need random weights.

i'm sure there is an easy way but since i'm new to matlab and after looking for a long time i figured i ask the community.

thanks for your help.

Answer 1

[the cyclist]

Use Roger Stafford's solution from the FEX: http://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum

The method assures good statistical properties for the marginal probabilities, and a uniform distribution across the joint probability space. All good things.

If you download Roger's code, I suggest you run this test to compare methods. (I'll post a figure with the result later, if I can.)

% Roger Stafford's solution
B1 = randfixedsum(10,10000,1,0,1);

% "Easy method" [Please don't use!]
A = rand(100000,10);
B2 = bsxfun(@rdivide,A,sum(A,2));

% Compare the marginal distributions of one variable
figure
subplot(2,1,1),hist(B1(1,:),25)
subplot(2,1,2),hist(B2(:,1),25)

Answer 2

[Sean de Wolski]

Easiest way is to normalize by the sum:

A = rand(1,10);
B=A./sum(A);
sum(B)

However, there are some things that make this non-truly random. If you care:

FEX:Roger's:randfixedsum

[the cyclist]

I highly recommend using Roger Stafford's FEX contribution, and not taking the "easy way out".

[Sean de Wolski]

It really depends on the use case. For a homework problem, I would take the easy way out.

[Matthias]

thanks again both of you for the answers provided.