我意识到正态分布是无限的.我猜尾巴可以被截断,所以当一个随机值计算在范围之外时,重新计算.这提高了整数在该范围内的概率,但是只要该效果是可以忍受的(<5％),这是很好的.

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); 
    }
}

我可能需要将标准差缩小到一定程度上,但不了解如何.

回答：

// 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;
    }