C＃：数值算法生成的二项分布数 [英] C#: Numerical algorithm to generate numbers from Binomial distribution

问题描述

我需要从二项式（N，P）分布生成随机数。

I need to generate random numbers from Binomial(n,p) distribution.

一个二项式（N，P）随机变量是取n统一变量的总和1以概率p。在伪代码， X = 0;对于（I = 0; I&下; N ++ⅰ）X + =（RAND（）&下，P？1：0）;将生成一个二项式（N，P）

A Binomial(n,p) random variable is sum of n uniform variables which take 1 with probability p. In pseudo code, x=0; for(i=0; i<n; ++i) x+=(rand()<p?1:0); will generate a Binomial(n,p).

我需要生成这对小以至真大N，例如N = 10 ^ 6和p = 0.02 。有没有快速的数值算法来生成它。

I need to generate this for small as well as really large n, for example n = 10^6 and p=0.02. Is there any fast numerical algorithm to generate it?

编辑 - ？

现在这是我的近似（以及用于精确泊松分布和正态分布函数） -

Right now this is what I have as approximation (along with functions for exact Poisson and Normal distribution)-

    public long Binomial(long n, double p) {
        // As of now it is an approximation
        if (n < 1000) {
            long result = 0;
            for (int i=0; i<n; ++i)
                if (random.NextDouble() < p) result++;
            return result;
        }
        if (n * p < 10) return Poisson(n * p);
        else if (n * (1 - p) < 10) return n - Poisson(n * p);
        else {
            long v = (long)(0.5 + nextNormal(n * p, Math.Sqrt(n * p * (1 - p))));
            if (v < 0) v = 0;
            else if (v > n) v = n;
            return v;
        }
    }

推荐答案

如果你愿意支付，然后看看的 NMath 通过Centerspace。

If you are willing to pay, then take a look at NMath by Centerspace.

否则由统计程序R用于C代码是这里，而应该是简单地移植到C＃

Otherwise, the C code used by the Stats program R is here, and should be straightforward to port to C#.

编辑：有细节上的实用数值方法与杰克徐C＃。

另一个编辑：一个免费的C＃库，你想要做什么

ANOTHER A free C# library that does what you want.

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