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 Roulette Selection in Genetic Algorithms
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