Selecting a "random" element from an array with each element having it's own weighting

Hi,

I am trying to write code that will permit me to select a "random" element from an array with each element having it's own weighting.

For example, assume array A = [1;2;3;4], where there is a 10% chance for 1, 20% chance for 2, 30% chance for 3 and 40% chance for 4 to be chosen.

I suppose I could just have number 2 added twice, number 3 three times and 4 four times, but trying to find something more robust since the data I'm working with is very large.

How would I go about writing this code?

Thanks

Answer 1

[Bruno Luong]

A=[1,2,3,4];
p=[10 20 30 40];

c=cumsum(p);
[~,r]=histc(rand(1,1e6),[0 c/c(end)]); % generate 1e6 numbers
r=A(r);

% Check
histogram(r)

[Matlab Beginner]

So how would I actually take a random sample from A?

[Bruno Luong]

It's "r" 1e6 random samples from A.

[Matlab Beginner]

I just need 1 random sample though

[Bruno Luong]

Change 1e6 in the code to 1 or to whatever the number of samples you wish.

[Matlab Beginner]

That's great, thanks for clarifying!

[Matlab Beginner]

What if I now have a requirement that means only the 3rd and 4th element can be selected? Preferably without having to change the % probability value of each (or recalculating the CDF again).

[Matlab Beginner]

@Bruno Luong

Answer 2

[Jeff Miller]

% Wts is your vector of weights.
Wts = Wts / sum(Wts);  % make sure they sum to 1
cumPrs = cumsum(Wts);  % cumPr is the cumulative probability of selecting each vector position or smaller
r = rand;  % a random number between 0 and 1
randVecPos = find(cumPrs>r,1);  % select this random vector position from your array

[Matlab Beginner]

A=[1,2,3,4];
Wts = [0.1,0.4,0.3,0.2];
cumPrs = cumsum(Wts);  
r = rand;
randVecPos = find(r>cumPrs,1)

So if I assume 1 has 10% chance of being selected, 2 has 40% chance, etc.

If I use above code I always get 1 as the value for randVecPos

[Jeff Miller]

sorry, that should be cumPrs>r

[Matlab Beginner]

Perfect, thank you!

[Bruno Luong]

This code is buggy, it returns empty with 10% chance.

Need to put 0 in front of the array of FIND command as with my code.