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=[0.005 0.01 0.015 0.02]; 

suppsize_epsilon=size(supp_epsilon,2);

pr_mass_epsilon=zeros(suppsize_epsilon,1);

alpha=1;
beta=4;

for j=1:suppsize_epsilon
    pr_mass_epsilon(j)=betacdf(supp_epsilon(j),alpha,beta)/sum(betacdf(supp_epsilon,alpha,beta));
end

Note that the components of pr_mass_epsilon sum up to 1. Now, I want to draw n random numbers from pr_mass_epsilon. How can I do this? I would like a code that works for any suppsize_epsilon.

In other words: I want to randomly draw elements from supp_epsilon, each element with a probability given by pr_mass_epsilon.

Efficacious

Related question on vectorization of this question: https://mcmap.net/q/540953/-how-do-i-create-a-vectorized-version-of-randsample-in-matlab/8239061 – Manganin

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')

Boulogne

Both the answers here (with & without toolboxes) are superior to this question and this one both in simplicity and accessibility. – Manganin

@Manganin Good find. Do you think this should be marked as a duplicate of the second one you linked? The only difference is the population of values – Boulogne

I flagged both of those as duplicates of this one (this really should be the target) as they both deal with generating discrete random variables from a probability mass function. So no, my opinion is they should be dupes of this one. – Manganin

Thanks, I have posted a related question for vectors now #58632301 – Efficacious