有没有一个C＃库，将执行Excel NORMINV函数？
我正在运行一些蒙特卡洛模拟，并使用Office Interrop广泛使用Excel函数NORM.INV。 这个函数有三个参数（概率，平均值，标准差），并返回累积分布的倒数。
我想将我的代码移动到一个Web应用程序，但这将需要在服务器上安装Excel。 有谁知道一个C＃统计库有一个等效的functionNORM.INV？
Meta.Numerics正是你正在寻找的。 这是使用该库的代码：
Distribution n = new NormalDistribution(mean, standardDeviation); double x = n.InverseLeftProbability(probability); 如果你这样做是为了产生正常的偏差，GetRandomValue函数甚至更快。
我还需要一个NORMINV的C＃实现，最接近我发现是一个C ++实现http://www.wilmott.com/messageview.cfm?catid=10&threadid=38771 ，所以我做了一个快速和脏的翻译到C＃，这里的细节http://weblogs.asp.net/esanchez/archive/2010/07/29/a-quick-and-dirty-implementation-of-excel-norminv-function-in-c.aspx 。 我只做了几个基本的testing，所以要小心，如果你决定使用它，无论如何，希望它有帮助！
这里描述了包括系数的逆法向CDF。 相对误差的绝对值小于1.15×10-9
public static class NormalDistributionConfidenceCalculator { /// <summary> /// /// </summary> public static double InverseNormalDistribution(double probability, double min, double max) { double x = 0; double a = 0; double b = 1; double precision = Math.Pow(10, -3); while ((b - a) > precision) { x = (a + b) / 2; if (NormInv(x) > probability) { b = x; } else { a = x; } } if ((max > 0) && (min > 0)) { x = x * (max - min) + min; } return x; } /// <summary> /// Returns the cumulative density function evaluated at A given value. /// </summary> /// <param name="x">A position on the x-axis.</param> /// <param name="mean"></param> /// <param name="sigma"></param> /// <returns>The cumulative density function evaluated at <C>x</C>.</returns> /// <remarks>The value of the cumulative density function at A point <C>x</C> is /// probability that the value of A random variable having this normal density is /// less than or equal to <C>x</C>. /// </remarks> public static double NormalDistribution(double x, double mean, double sigma) { // This algorithm is ported from dcdflib: // Cody, WD (1993). "ALGORITHM 715: SPECFUN - A Portabel FORTRAN // Package of Special Function Routines and Test Drivers" // acm Transactions on Mathematical Software. 19, 22-32. int i; double del, xden, xnum, xsq; double result, ccum; double arg = (x - mean) / sigma; const double sixten = 1.60e0; const double sqrpi = 3.9894228040143267794e-1; const double thrsh = 0.66291e0; const double root32 = 5.656854248e0; const double zero = 0.0e0; const double min = Double.Epsilon; double z = arg; double y = Math.Abs(z); const double half = 0.5e0; const double one = 1.0e0; double[] a = { 2.2352520354606839287e00, 1.6102823106855587881e02, 1.0676894854603709582e03, 1.8154981253343561249e04, 6.5682337918207449113e-2 }; double[] b = { 4.7202581904688241870e01, 9.7609855173777669322e02, 1.0260932208618978205e04, 4.5507789335026729956e04 }; double[] c = { 3.9894151208813466764e-1, 8.8831497943883759412e00, 9.3506656132177855979e01, 5.9727027639480026226e02, 2.4945375852903726711e03, 6.8481904505362823326e03, 1.1602651437647350124e04, 9.8427148383839780218e03, 1.0765576773720192317e-8 }; double[] d = { 2.2266688044328115691e01, 2.3538790178262499861e02, 1.5193775994075548050e03, 6.4855582982667607550e03, 1.8615571640885098091e04, 3.4900952721145977266e04, 3.8912003286093271411e04, 1.9685429676859990727e04 }; double[] p = { 2.1589853405795699e-1, 1.274011611602473639e-1, 2.2235277870649807e-2, 1.421619193227893466e-3, 2.9112874951168792e-5, 2.307344176494017303e-2 }; double[] q = { 1.28426009614491121e00, 4.68238212480865118e-1, 6.59881378689285515e-2, 3.78239633202758244e-3, 7.29751555083966205e-5 }; if (y <= thrsh) { // // Evaluate anorm for |X| <= 0.66291 // xsq = zero; if (y > double.Epsilon) xsq = z * z; xnum = a[4] * xsq; xden = xsq; for (i = 0; i < 3; i++) { xnum = (xnum + a[i]) * xsq; xden = (xden + b[i]) * xsq; } result = z * (xnum + a[3]) / (xden + b[3]); double temp = result; result = half + temp; } // // Evaluate anorm for 0.66291 <= |X| <= sqrt(32) // else if (y <= root32) { xnum = c[8] * y; xden = y; for (i = 0; i < 7; i++) { xnum = (xnum + c[i]) * y; xden = (xden + d[i]) * y; } result = (xnum + c[7]) / (xden + d[7]); xsq = Math.Floor(y * sixten) / sixten; del = (y - xsq) * (y + xsq); result = Math.Exp(-(xsq * xsq * half)) * Math.Exp(-(del * half)) * result; ccum = one - result; if (z > zero) { result = ccum; } } // // Evaluate anorm for |X| > sqrt(32) // else { xsq = one / (z * z); xnum = p[5] * xsq; xden = xsq; for (i = 0; i < 4; i++) { xnum = (xnum + p[i]) * xsq; xden = (xden + q[i]) * xsq; } result = xsq * (xnum + p[4]) / (xden + q[4]); result = (sqrpi - result) / y; xsq = Math.Floor(z * sixten) / sixten; del = (z - xsq) * (z + xsq); result = Math.Exp(-(xsq * xsq * half)) * Math.Exp(-(del * half)) * result; ccum = one - result; if (z > zero) { result = ccum; } } if (result < min) result = 0.0e0; return result; } /// <summary> /// Given a probability, a mean, and a standard deviation, an x value can be calculated. /// </summary> /// <returns></returns> public static double NormInv(double probability) { const double a1 = -39.6968302866538; const double a2 = 220.946098424521; const double a3 = -275.928510446969; const double a4 = 138.357751867269; const double a5 = -30.6647980661472; const double a6 = 2.50662827745924; const double b1 = -54.4760987982241; const double b2 = 161.585836858041; const double b3 = -155.698979859887; const double b4 = 66.8013118877197; const double b5 = -13.2806815528857; const double c1 = -7.78489400243029E-03; const double c2 = -0.322396458041136; const double c3 = -2.40075827716184; const double c4 = -2.54973253934373; const double c5 = 4.37466414146497; const double c6 = 2.93816398269878; const double d1 = 7.78469570904146E-03; const double d2 = 0.32246712907004; const double d3 = 2.445134137143; const double d4 = 3.75440866190742; //Define break-points // using Epsilon is wrong; see link above for reference to 0.02425 value //const double pLow = double.Epsilon; const double pLow = 0.02425; const double pHigh = 1 - pLow; //Define work variables double q; double result = 0; // if argument out of bounds. // set it to a value within desired precision. if (probability <= 0) probability = pLow; if (probability >= 1) probability = pHigh; if (probability < pLow) { //Rational approximation for lower region q = Math.Sqrt(-2 * Math.Log(probability)); result = (((((c1 * q + c2) * q + c3) * q + c4) * q + c5) * q + c6) / ((((d1 * q + d2) * q + d3) * q + d4) * q + 1); } else if (probability <= pHigh) { //Rational approximation for lower region q = probability - 0.5; double r = q * q; result = (((((a1 * r + a2) * r + a3) * r + a4) * r + a5) * r + a6) * q / (((((b1 * r + b2) * r + b3) * r + b4) * r + b5) * r + 1); } else if (probability < 1) { //Rational approximation for upper region q = Math.Sqrt(-2 * Math.Log(1 - probability)); result = -(((((c1 * q + c2) * q + c3) * q + c4) * q + c5) * q + c6) / ((((d1 * q + d2) * q + d3) * q + d4) * q + 1); } return result; } /// <summary> /// /// </summary> /// <param name="probability"></param> /// <param name="mean"></param> /// <param name="sigma"></param> /// <returns></returns> public static double NormInv(double probability, double mean, double sigma) { double x = NormInv(probability); return sigma * x + mean; } }
我不知道一个图书馆，但发现这个链接 – http://home.online.no/~pjacklam/notes/invnorm/ – 描述一个algorithm。 它有多种语言的实现，但不是C＃。 你可以使用VB.NET版本，或自己移植它。
也许你可以尝试这个组件， http://www.smartxls.com ，它有一个Excel兼容的运行时计算引擎，它不需要安装Excel。
添加图表控件
double result = Chart1.DataManipulator.Statistics.InverseNormalDistribution（probability）;
概率例如：0.9，0.4