Non-Uniform Random Number Generator Implementation

Question

I need a random number generator that picks numbers over a specified range with a programmable mean.

For example, I need to pick numbers between 2 and 14 and I need the average of the random numbers to be 5.

I use random number generators a lot. Usually I just need a uniform distribution.

I don't even know what to call this type of distribution.

Thank you for any assistance or insight you can provide.

Answer 1

You might be able to use a binomial distribution, if you're happy with the shape of that distribution. Set n=12 and p=0.25. This will give you a value between 0 and 12 with a mean of 3. Just add 2 to each result to get the range and mean you are looking for.

Edit: As for implementation, you can probably find a library for your chosen language that supports non-uniform distributions (I've written one myself for Java).

A binomial distribution can be approximated fairly easily using a uniform RNG. Simply perform n trials and record the number of successes. So if you have n=10 and p=0.5, it's just like flipping a coin 10 times in a row and counting the number of heads. For p=0.25 just generate uniformly-distributed values between 0 and 3 and only count zeros as successes.

If you want a more efficient implementation, there is a clever algorithm hidden away in the exercises of volume 2 of Knuth's The Art of Computer Programming.

Answer 2

You haven't said what distribution you are after. Regarding your specific example, a function which produced a uniform distribution between 2 and 8 would satisfy your requirements, strictly as you have written them :)

Answer 3

Based on the Wikipedia sub-article about non-uniform generators, it would seem you want to apply the output of a uniform pseudorandom number generator to an area distribution that meets the desired mean.

Answer 4

If you want a non-uniform distribution of the random number, then you might have to implement some sort of mapping, e.g:

// returns a number between 0..5 with a custom distribution
int MyCustomDistribution()
{
  int r = rand(100); // random number between 0..100
  if (r < 10) return 1;
  if (r < 30) return 2;
  if (r < 42) return 3;
  ...
}

Answer 5

Assign all numbers equal probabilities,

while currentAverage not equal to intendedAverage (whithin possible margin)

 pickedNumber = pick one of the possible numbers (at random, uniform probability, if you pick intendedAverage pick again)

 if (pickedNumber is greater than intendedAverage and currentAverage<intendedAverage) or (pickedNumber is less than intendedAverage and currentAverage>intendedAverage)

   increase pickedNumber's probability by delta at the expense of all others, conserving sum=100%

 else

   decrease pickedNumber's probability by delta to the benefit of all others, conserving sum=100%

 end if

 delta=0.98*delta (the rate of decrease of delta should probably be experimented with)

end while

Answer 6

You can create a non-uniform PRNG from a uniform one. This makes sense, as you can imagine taking a uniform PRNG that returns 0,1,2 and create a new, non-uniform PRNG by returning 0 for values 0,1 and 1 for the value 2.

There is more to it if you want specific characteristics on the distribution of your new, non-uniform PRNG. This is covered on the Wikipedia page on PRNGs, and the Ziggurat algorithm is specifically mentioned.

With those clues you should be able to search up some code.