MATLAB: How to generate uniformly distributed weights between intervals that sum to one

random number generatoruniformweight

Hi, I have three weight intervals: w1=[0.25,0.50] w2=[0.15,0.40] w3=[0.20,0.60]

How can I generate 1000 random weight vectors (uniform distribution) Weight_vector=(w1,w2,w3) that each Wi correspond to related interval and they sum to one? Two examples:

Weight_vector1: (0.25,0.25,0.50);

Weight_vector2: (0.30,0.15,0.55);

Thanks, Hossein

Best Answer

For general sets of intervals, randfixedsum does not work. For this reason I provided randFixedLinearCombination . It handles a much more general problem than randfixedsum, although for large numbers of variables, it will not be as efficient as randfixedsum.

n = 10;
lb = [.25 .15 .20];
ub = [.5 .4 .6];
linearCombination = [1 1 1];
rhs = 1;
xyz = randFixedLinearCombination(n,rhs,linearCombination,lb,ub)
xyz =
         0.276646000258171         0.397179072324999          0.32617492741683
         0.479429538804855          0.25335926183292         0.267211199362225
         0.436921197465117         0.310210767126349         0.252868035408533
         0.473906980805434         0.168956179849817         0.357136839344749
         0.397453211716306         0.257931038823466         0.344615749460228
         0.370300633544778           0.3798772062265         0.249822160228722
         0.291816855265393         0.393117202614066         0.315065942120541
         0.355210364802235         0.336898845478376         0.307890789719389
         0.453532562192296         0.261548824228386         0.284918613579318
         0.300587077933784         0.256205660055041         0.443207262011175
sum(xyz,2)
ans =
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1

As you can see, each row sums to 1. Each column lies within the lower and upper bounds for that variable.

Related Solutions

MATLAB: How can calculate this formula with matlab

You can pull the w_i and sigma_i outside of the sum_j, because the don't depend on j. And you can compute the sum_j nicely as a matrix multiplication of row vector w and column vector sigma.

w = rand(1,10); % sample values for w and s
s = rand(10, 1);
N = numel(w);
y = 0; 
for i=1:N-1
  y = y + s(i)*w(i)* w(i+1:end)*s(i+1:end);
end
y = 2*y;

MATLAB: Random positive numbers with constant sum

First of all, there is no such thing as a random positive number. If you don't define the distribution, then it is meaningless to talk about a random number.

And you can't have a uniform random number on the interval (0,inf].

You CAN define a uniform random number on A BOUNDED SET. So, the interval[0,1]. But if you want to constrain the sum to be constant, then be careful. This question gets asked over and over again, and people answer it thinking you can solve it trivially. They generate a vector of numbers, and then scale them so the sum is the desired value. WRONG. This generates a distribution that is not in fact uniform.

So use a tool like randfixedsum , as found on the file exchange, or my own randFixedLinearCombination , also on the file exchange.

The latter tool is more capable for some problems, but for long vectors that sum to a constant, it will be inefficient. It probably won't work well in more than about 6 dimensions. But randfixedsum is fine beyond that point.

So to generate a set of 10 numbers that sum to 4, where each element in the vector is in the interval [.2, .6], is as simple as:

S = randfixedsum(10,1,4,.2,.6)
S =
    0.4354
    0.5535
    0.2221
    0.3235
    0.4106
    0.5368
    0.3963
    0.2636
    0.4705
    0.3877
sum(S)
ans =
    4.0000

Again, DON'T use a rescaling scheme. Randfixedsum is perfect for the problem.

Best Answer

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MATLAB: How can calculate this formula with matlab

MATLAB: Random positive numbers with constant sum

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