How can I create a weighted random number.

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 <= 10000; i++)

{

number = WeightedRandomNumber(1, 9, 5);

numbers[number - 1]++;

}

// display their frequencies

for(int i = 0; i < numbers.Length; 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;

{

// get random integer between min and max

num = rand.Next(min, max + 1);

// calculate the weight of the random integer(mostLikely = 100).

if (num <= mostLikely)

{

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

1 Reply

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Vulpes14y ago
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 <= 10000; i++)
{
number = WeightedRandomNumber(1, 9, 5);
numbers[number - 1]++;
}

// display their frequencies
for(int i = 0; i < numbers.Length; 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 <= mostLikely)
{
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
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