如何寫出常態分配

Question

想請教各位：
                   我現要做模擬問題,請問我該如何才能產生 常態分配的樣本？
                                                                                                                謝謝

Answer 1

參考: Normal distribution, error function

Answer 2

一般我是用數學手冊跟統計學書上記載的近似式：

Code Snippet

Private Function CDFofNormal(ByVal z)

tz = Abs(z)
b = 0.5 * (1 + 0.196854 * tz + 0.115194 * tz ^ 2 + 0.000344 * tz ^ 3 + 0.019527 * tz ^ 4) ^ (-4)
If z >= 0 Then b = 1 - b
CDFofNormal = b

End Function

 

 

不會用太複雜的方式去近似。

Answer 3

msdn 論壇的解答: Re: Normal Distribution

public double CND(double X)

{

    double L = 0.0;

    double K = 0.0;

    double dCND = 0.0;

    const double a1 = 0.31938153;

    const double a2 = -0.356563782;

    const double a3 = 1.781477937;

    const double a4 = -1.821255978;

    const double a5 = 1.330274429;

    L = Math.Abs(X);

    K = 1.0/(1.0 + 0.2316419*L);

    dCND = 1.0 - 1.0/Math.Sqrt(2*Convert.ToDouble(Math.PI.ToString()))*Math.Exp(-L*L/2.0)*(a1*K + a2*K*K + a3*Math.Pow(K, 3.0) + a4*Math.Pow(K, 4.0) + a5*Math.Pow(K, 5.0));

    if (X < 0)

    {

        return 1.0 - dCND;

    }

    else

    {

        return dCND;

    }

}