Java實現Excel中的NORMSDIST函數和NORMSINV函數

由於工作中需要將Excel中的此兩種函數轉換成java函數，從而計算內部評級的資本占用率和資本占用金額。經過多方查閱資料和整理，總結出如下兩個轉換方法

標准正態分布累計函數NORMSDIST：

public static double NormSDist(double z) {
        // this guards against overflow
        if (z > 6)
            return 1;
        if (z < -6)
            return 0;

        double  gamma = 0.231641900, 
                a1 = 0.319381530, 
                a2 = -0.356563782, 
                a3 = 1.781477973, 
                a4 = -1.821255978, 
                a5 = 1.330274429;

        double x = Math.abs(z);
        double t = 1 / (1 + gamma * x);


        double n = 1
                - (1 / (Math.sqrt(2 * Math.PI)) * Math.exp(-z * z / 2))
                * (a1 * t + a2 * Math.pow(t, 2) + a3 * Math.pow(t, 3) + a4
                        * Math.pow(t, 4) + a5 * Math.pow(t, 5));
        if (z < 0)
            return 1.0 - n;

        return n;
    }

標准正態分布累計反函數NORMSINV：

public static double normsinv(double p) {
        double LOW = 0.02425;
        double HIGH = 0.97575;

        double a[] = { -3.969683028665376e+01, 2.209460984245205e+02,
                -2.759285104469687e+02, 1.383577518672690e+02,
                -3.066479806614716e+01, 2.506628277459239e+00 };

        double b[] = { -5.447609879822406e+01, 1.615858368580409e+02,
                -1.556989798598866e+02, 6.680131188771972e+01,
                -1.328068155288572e+01 };

        double c[] = { -7.784894002430293e-03, -3.223964580411365e-01,
                -2.400758277161838e+00, -2.549732539343734e+00,
                4.374664141464968e+00, 2.938163982698783e+00 };

        double d[] = { 7.784695709041462e-03, 3.224671290700398e-01,
                2.445134137142996e+00, 3.754408661907416e+00 };

        double q, r;

        if (p < LOW) {
            q = Math.sqrt(-2 * Math.log(p));
            return (((((c[0] * q + c[1]) * q + c[2]) * q + c[3]) * q + c[4])
                    * q + c[5])
                    / ((((d[0] * q + d[1]) * q + d[2]) * q + d[3]) * q + 1);
        } else if (p > HIGH) {
            q = Math.sqrt(-2 * Math.log(1 - p));
            return -(((((c[0] * q + c[1]) * q + c[2]) * q + c[3]) * q + c[4])
                    * q + c[5])
                    / ((((d[0] * q + d[1]) * q + d[2]) * q + d[3]) * q + 1);
        } else {
            q = p - 0.5;
            r = q * q;
            return (((((a[0] * r + a[1]) * r + a[2]) * r + a[3]) * r + a[4])
                    * r + a[5])
                    * q
                    / (((((b[0] * r + b[1]) * r + b[2]) * r + b[3]) * r + b[4])
                            * r + 1);
        }
    }

不足之處，敬請指出