Draw random numbers from pre-specified probability mass function in Matlab

Question

I have a support (supp_epsilon) and a probability mass function (pr_mass_epsilon) in Matlab, constructed as follows.

supp_epsilon=[         


        

Answer 1

Using the Statistics Toolbox

The randsample function can do that directly:

result = randsample(supp_epsilon, n, true, pr_mass_epsilon);

Without using toolboxes

Manual approach:

1. Generate n samples of a uniform random variable in the interval (0,1).
2. Compare each sample with the distribution function (cumulative sum of mass function).
3. See in which interval of the distribution function each uniform sample lies.
4. Index into the array of possible values

result = supp_epsilon(sum(rand(1,n)>cumsum(pr_mass_epsilon(:)), 1)+1);

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For your example, with n=1e6 either of the two approaches gives a histogram similar to this:

histogram(result, 'normalization', 'probability')