Given the start and the end of an integer range, how do I calculate a normally distributed random integer between this range?
I realize that the normal distribution goes into -+ infinity. I guess the tails can be cutoff, so when a random gets computed outside the range, recompute. This elevates the probability of integers in the range, but as long as the this effect is tolerable (<5%), it's fine.
public class Gaussian
{
private static bool uselast = true;
private static double next_gaussian = 0.0;
private static Random random = new Random();
public static double BoxMuller()
{
if (uselast)
{
uselast = false;
return next_gaussian;
}
else
{
double v1, v2, s;
do
{
v1 = 2.0 * random.NextDouble() - 1.0;
v2 = 2.0 * random.NextDouble() - 1.0;
s = v1 * v1 + v2 * v2;
} while (s >= 1.0 || s == 0);
s = System.Math.Sqrt((-2.0 * System.Math.Log(s)) / s);
next_gaussian = v2 * s;
uselast = true;
return v1 * s;
}
}
public static double BoxMuller(double mean, double standard_deviation)
{
return mean + BoxMuller() * standard_deviation;
}
public static int Next(int min, int max)
{
return (int)BoxMuller(min + (max - min) / 2.0, 1.0);
}
}
I probably need to scale the standard deviation some how relative to the range, but don't understand how.
Answer:
// Will approximitely give a random gaussian integer between min and max so that min and max are at
// 3.5 deviations from the mean (half-way of min and max).
public static int Next(int min, int max)
{
double deviations = 3.5;
int r;
while ((r = (int)BoxMuller(min + (max - min) / 2.0, (max - min) / 2.0 / deviations)) > max || r < min)
{
}
return r;
}