正态分布随机数

NormalDistribution.cs

using System;

public class NormalDistribution
{
    private static Random random = new Random();

    /// <summary>
    /// 理论上这个函数的返回值范围是 正无穷到负无穷，但
    /// 约99.7%的数据位于均值的三个标准差范围内 ( 即 mu ± 3sigma )。
    /// </summary>
    /// <param name="mu"></param>
    /// <param name="sigma"></param>
    /// <returns></returns>
    public static double NextGaussian(double mu = 0, double sigma = 1)
    {
        // Generate two uniform random variables
        double u1 = random.NextDouble(); // Uniform(0,1] random doubles
        double u2 = random.NextDouble();

        // Use Box-Muller transform to generate two independent standard normally distributed normal variables
        // See https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
        double R = Math.Sqrt(-2.0 * Math.Log(u1));
        double theta = 2.0 * Math.PI * u2;
        double z = R * Math.Cos(theta); // Random normal(0,1)

        // Scale and shift to get desired mean and standard deviation
        return z * sigma + mu;
    }
    
    /// <summary>
    /// clamp01, include 0 and 1
    /// </summary>
    /// <returns></returns>
    public static double NextGaussian01()
    {
        return Math.Clamp((NextGaussian() + 4) / 8, 0, 1);
    }
}