How can I create a weighted random number.

Question

Ok this is getting me confused.

I need to creat e random number. usually not an issue. I need to be able to pass 3 paramaters though

a minimum, a maximum and a most likely.

the further away from the most likely you get the less chance that number has of actually showing.

Any idea on how I can accomplish this or even any tips?

Vulpes · Answer

As long as you use linear probabilities this is easier than it sounds but as well as the 3 parameters you need to assign weights to the minimum and maximum values relative to the most likely value so you know the relative probability of these values (and hence intermediate values) occurring. Here's some code to do this (.NET 4.0 or later) which uses integer arithmetic throughout for simplicity (just change to double if you need random decimal numbers). The code generates 10000 random numbers between 1 and 9 with a most likely value of 5. Default weights of 20 are used for the minimum and maximum values relative to a weight of 100 for the most likely number: using System; class Test { static Random rand = new Random(); static void Main() { // get ten thousand random numbers between 1 and 9 and count their frequencies int number; int[] numbers = new int[9]; for(int i = 1; i { number = WeightedRandomNumber(1 9 5); numbers[number - 1]++; } // display their frequencies for(int i = 0; i { Console.WriteLine({0} frequency = {1} i + 1 numbers[i]); } Console.ReadKey(); } static int WeightedRandomNumber(int min int max int mostLikely int minWeight = 20 int maxWeight = 20) { int num weight randomWeight; do { // get random integer between min and max num = rand.Next(min max + 1); // calculate the weight of the random integer(mostLikely = 100). if (num { weight = ((mostLikely - num) * minWeight + (num - min) * 100)/(mostLikely - min); } else { weight = ((num - mostLikely) * maxWeight + (max - num) * 100)/(max - mostLikely); } // get a random weight between 0 and 100 randomWeight = rand.Next(0 101); // between 0 and 100 // if the random weight is less than or equal to the random number's weight // then accept it otherwise get another random number } while(randomWeight > weight); return num; } } A typical result from running this program: 1 frequency = 420 2 frequency = 759 3 frequency = 1186 4 frequency = 1554 5 frequency = 2015 6 frequency = 1603 7 frequency = 1170 8 frequency = 845 9 frequency = 448 This compares with the 'expected' values of: 1 frequency = 400 2 frequency = 800 3 frequency = 1200 4 frequency = 1600 5 frequency = 2000 6 frequency = 1600 7 frequency = 1200 8 frequency = 800 9 frequency = 400