how to implement non uniform probability distribution?

Question

I am trying to implement non-uniform probability distribution in genetic algorithm.

In the implementation of genetic program, I have an experiment which has 3 outcomes, where each outcome has different probabilities. Let say, probablity of one outcome is 0.85, other is 0.01 and last one is 0.14?

P.S: i recently came to know that it is called non-uniform distribution of probability. I'm implementing it in Java, can anyone tell the theory behind non-uniform prob. distribution & also any Java packages implementing it.

Feel free to ask me know, if u need any more information on the problem!

Thanks in advance!

Answer 1

For a simple discrete distribution, you can write a sampler that will return your outcomes with the desired frequency by using the cumulative probabilities.

Random r = new Random();
double v = r.nextDouble();

if (v <= 0.85) { return 0; }
if (v <= 0.86) { return 1; }
return 2;

This will return the numbers 0, 1 and 2 with a probability of 0.85, 0.01 and 0.14.

As far as the theory on non-uniform probability distributions, you can start with this Wikipedia article on probability distributions; take special note of the collapsible sections at the bottom of the page. You will find that there are dozens of non-uniform distribution (both continuous and discrete) with different properties.

Answer 2

In your particular case it is better to get a random value in [0; 100) using uniform distribution and then check what range it falls in: [0; 85), [85;99), [99, 100)

Answer 3

Based on your description it seems to me that you are talking about fitness proportionate selection (also known as roulette wheel selection).
http://en.wikipedia.org/wiki/Roulette-wheel_selection

I think nailxx' answer is a pretty compact description what you need to do.

see also http://stackoverflow.com/questions/177271/roulette-selection-in-genetic-algorithms
http://stackoverflow.com/questions/298301/roulette-wheel-selection-algorithm

If I'm wrong here are some libraries that you may find useful:
http://www.ee.ucl.ac.uk/~mflanaga/java/Stat.html
http://commons.apache.org/math/apidocs/org/apache/commons/math/random/package-summary.html