select random number from an array with probabilities

I have an array of three element: S=[4 3.9 3.8] and I want to randomly select one of those three numbers. The probability of selecting 4 is 0.5, the probability of selecting 3.9 is 0.4 and the probability of selecting 3.8 is 0.1.

Can anyone help me please?

[Adam]

Off the top of my head and unverified because my Matlab is busy and I can't be bothered to start another one:

cumulativeProbs = cumsum( [0.5 0.4 0.1] );
S( find( rand > cumulativeProbs, 1 ) - 1 );

Answer 1

[Sky Sartorius]

You can query the cumulative probabilities:

S = [4, 3.9, 3.8];
w = [0.5, 0.4, 0.1];
w = w/sum(w); % Make sure probabilites add up to 1.
cp = [0, cumsum(w)];
r = rand;
ind = find(r>cp, 1, 'last');
result = S(ind)

[Margherita Premoli]

thanks a lot! But why did you write r>cp in defining "ind" and why did you make it select the last indice and not the first as default?

[Margherita Premoli]

sorry to bother you again but why do we need the cumulative probability?

[Sky Sartorius]

For any probability distribution or set of probabilities (that add up to 1), the cumulative distribution function (CDF) will yield a result between 0 and 1. The random number generator also returns numbers between 0 and 1, so by mapping that to the output of the CDF, you can generate your values at the desired distribution. You can visualize:

S = [4, 3.9, 3.8];
w = [0.5, 0.4, 0.1];
w = w/sum(w); % Make sure probabilites add up to 1.
cp = [0, cumsum(w)];

plot(0:3,cp,'ok')
xlabel('Index')
ylabel('Cum. prob.')

figure
plot(cp,0:3)
xlabel('r')
ylabel('Index (take ceil of result)') % Ceil is also why find is 'r>cp' and 'last'.
title('Reverse CDF lookup')

[Margherita Premoli]

okay great, now it is clar! thanks again :)