在两个和等于给定数字的值之间得到n个不同的随机数

更新

通常,当人们问这样的问题时,有一个隐含的假设/要求——所有随机数都应该以相同的方式分布。这意味着,如果我从抽样数组中为索引为0的项绘制边际概率密度函数(pdf),我将得到与我为数组中最后一项绘制边际概率密度函数相同的分布。人们通常对随机数组进行抽样,然后将其传递给其他例程来做一些有趣的事情。如果项目0的边际PDF与上一个索引项目的边际PDF不同,则仅恢复数组将产生与使用此类随机值的代码截然不同的结果。


在这里,我使用我的采样程序,绘制了原始条件下([-50…50]和=300)项目0和最后一个项目(29)的随机数分布。看起来很像,不是吗?



好的,这是您的采样程序的图片,相同的原始条件([-50…50]和=300),相同的样本数



更新II

用户应该检查采样例程的返回值,如果(并且仅当)返回值为真,则接受并使用采样数组。这是接受/拒绝方法。如图所示,下面是用于柱状图样本的代码:

int[]hh=new int[100];//已分配柱状图














AB



MathDotNet



using System;

using MathNet.Numerics.Distributions;
using MathNet.Numerics.Random;

class Program
{
    static void SampleDirichlet(double alpha, double[] rn)
    {
        if (rn == null)
            throw new ArgumentException("SampleDirichlet:: Results placeholder is null");

        if (alpha <= 0.0)
            throw new ArgumentException($"SampleDirichlet:: alpha {alpha} is non-positive");

        int n = rn.Length;
        if (n == 0)
            throw new ArgumentException("SampleDirichlet:: Results placeholder is of zero size");

        var gamma = new Gamma(alpha, 1.0);

        double sum = 0.0;
        for(int k = 0; k != n; ++k) {
            double v = gamma.Sample();
            sum  += v;
            rn[k] = v;
        }

        if (sum <= 0.0)
            throw new ApplicationException($"SampleDirichlet:: sum {sum} is non-positive");

        // normalize
        sum = 1.0 / sum;
        for(int k = 0; k != n; ++k) {
            rn[k] *= sum;
        }
    }

    static bool SampleBoundedDirichlet(double alpha, double sum, double lo, double hi, double[] rn)
    {
        if (rn == null)
            throw new ArgumentException("SampleDirichlet:: Results placeholder is null");

        if (alpha <= 0.0)
            throw new ArgumentException($"SampleDirichlet:: alpha {alpha} is non-positive");

        if (lo >= hi)
            throw new ArgumentException($"SampleDirichlet:: low {lo} is larger than high {hi}");

        int n = rn.Length;
        if (n == 0)
            throw new ArgumentException("SampleDirichlet:: Results placeholder is of zero size");

        double mean = sum / (double)n;
        if (mean < lo || mean > hi)
            throw new ArgumentException($"SampleDirichlet:: mean value {mean} is not within [{lo}...{hi}] range");

        SampleDirichlet(alpha, rn);

        bool rc = true;
        for(int k = 0; k != n; ++k) {
            double v = lo + (mean - lo)*(double)n * rn[k];
            if (v > hi)
                rc = false;
            rn[k] = v;
        }
        return rc;
    }

    static void Main(string[] args)
    {
        double[] rn = new double [30];

        double lo = -50.0;
        double hi =  50.0;

        double alpha = 10.0;

        double sum = 300.0;

        for(int k = 0; k != 1_000; ++k) {
            var q = SampleBoundedDirichlet(alpha, sum, lo, hi, rn);
            Console.WriteLine($"Rng(BD), v = {q}");
            double s = 0.0;
            foreach(var r in rn) {
                Console.WriteLine($"Rng(BD),     r = {r}");
                s += r;
            }
            Console.WriteLine($"Rng(BD),    summa = {s}");
        }
    }
}


















        int[] hh = new int[100]; // histogram allocated

        var s = 1.0; // step size
        int k = 0;   // good samples counter
        for( ;; ) {
            var q = SampleBoundedDirichlet(alpha, sum, lo, hi, rn);
            if (q) // good sample, accept it
            {
                var v = rn[0]; // any index, 0 or 29 or ....
                var i = (int)((v - lo) / s);
                i = System.Math.Max(i, 0);
                i = System.Math.Min(i, hh.Length-1);
                hh[i] += 1;

                ++k;
                if (k == 100000) // required number of good samples reached
                    break;
            }
        }
        for(k = 0; k != hh.Length; ++k)
        {
            var x = lo + (double)k * s + 0.5*s;
            var v = hh[k];
            Console.WriteLine($"{x}     {v}");
        }