MATLAB: Generate random numbers given distribution/histogram

distributionhistogramrandomrandom number generator

MATLAB provides built-in functions to generate random numbers with an uniform or Gaussian (normal) distribution. My question is: if I have a discrete distribution or histogram, how can I can generate random numbers that have such a distribution (if the population (numbers I generate) is large enough)?
Please post here if anyone knows of a good method of doing this.
Thanks, David

Best Answer

Since nobody has any suggestions, here's one. If you have a discrete distribution, say it is a Nx2 matrix PD, first column the discrete values, second the probabilities of the corresponding value -- so sum(PD(:,2))==1.
Then map the probablities to the unit interval and use rand. What mean by that:
% Those are your values and the corr. probabilities:
PD =[
  1.0000    0.1000
  2.0000    0.3000
  3.0000    0.4000
  4.0000    0.2000];
% Then make it into a cumulative distribution
D = cumsum(PD(:,2));
% D = [0.1000    0.4000    0.8000    1.0000]'
Now for every r generated by rand, if it is between D(i) and D(i+1), then it corresponds to an outcome PD(1,i+1), with the obvious extension at i==0. Here's a way you could do that, even though I'm sure there are better ones:
R = rand(100,1); % Your trials
p = @(r) find(r<pd,1,'first'); % find the 1st index s.t. r<D(i);
% Now this are your results of the random trials
rR = arrayfun(p,R);
% Check whether the distribution looks right:  
hist(rR,1:4)
% It does, roughly 10% are 1, 30% are 2 and so on
If you want more help you should post a minimal example of the form in which you have the discrete distribution.
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