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

Answer 1

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 2

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 3

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.

Answer 4

My first idea would be:

• generate numbers in the range 0..1
• scale to the range -9..9 ( x-0.5; x*18)
• shift range by 5 -> -4 .. 14 (add 5)
• truncate the range to 2..14 (discard numbers < 2)

that should give you numbers in the range you want.

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

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.