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�l�计函数NormSDist和NormSInv函数实现

Dain — Tue, 13 Mar 2007 12:52:00 GMT

先说下今天写VBA学到的，那就是Excel的统计工作表函数�?br>Excel的统计工作表函数用于�Ҏ(gu��)��据区域进行统计分析。例如，�l�计工作表函数可以用来统计样本的方差、数据区间的频率分布�{�。是不是觉得好像是很专业范畴的东西？是的�Q�统计工作表函数中提供了(ji��n)很多属于�l�计学范畴的函数�Q�但也有些函数其实在你我的日常生�z�M��是很常用的，比如求班�U��^均成�l�，排名�{��?br>但是我的�E�序是要cpp实现上面俩个函数�Q�可是cpp没有�q�样的统计函数。查�?ji��n)好多资料，扑ֈ�了(ji��n)多��式�q�似的方法：(x��)
/***************************************************************/
/* �q�回标准正态分布的累积函数�Q�该分布的��^均��gؓ(f��) 0�Q�标准偏差�ؓ(f��) 1�?nbsp; */
/***************************************************************/
double NormSDist(const double z)
{
// this guards against overflow
if(z > 6) return 1;
if(z < -6) return 0;

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

double k = 1.0 / (1 + fabs(z) * gamma);
double n = k * (a1 + k * (a2 + k * (a3 + k * (a4 + k * a5))));
n = 1 - Normal(z) * n;
if(z < 0)
return 1.0 - n;

return n;
}

/***************************************************************/
/* �q�回标准正态分布篏�U�函数的逆函数。该分布的��^均��gؓ(f��) 0�Q�标准偏差�ؓ(f��) 1�?/font> */
/***************************************************************/
double normsinv(const double p)
{
static const double LOW = 0.02425;
static const double HIGH = 0.97575;

/* Coefficients in rational approximations. */
static const double a[] =
{
  -3.969683028665376e+01,
   2.209460984245205e+02,
  -2.759285104469687e+02,
   1.383577518672690e+02,
  -3.066479806614716e+01,
   2.506628277459239e+00
};

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

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

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

double q, r;

errno = 0;

if (p < 0 || p > 1)
{
  errno = EDOM;
  return 0.0;
}
else if (p == 0)
{
  errno = ERANGE;
  return -HUGE_VAL /* minus "infinity" */;
}
else if (p == 1)
{
  errno = ERANGE;
  return HUGE_VAL /* "infinity" */;
}
else if (p < LOW)
{
  /* Rational approximation for lower region */
  q = sqrt(-2*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)
{
  /* Rational approximation for upper region */
  q = sqrt(-2*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
{
  /* Rational approximation for central region */
      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);
}
}

Dain 2007-03-13 20:52 发表评论

Quasi-Monte Carlo(Korobov rule)

Dain — Mon, 12 Mar 2007 03:04:00 GMT

#include < cmath >
#include < vector >

using namespace std;

// Korobov rules
vector < vector < double > > korobov( int a, // base
                                                         int n, // sample size(a prime)
                                                         int t) // dimensional
{
    vector<double> G(t);
    vector< vector<double> > U(n,vector<double>(t)); // t-dimensional points

    int i,j;
    for(i = 0;i < t;i++)
        G[i] = pow(a,i) / (double)n;

    for(i = 0;i < n;i++)
        for (j = 0;j < t;j++)
        {
            U[i][j] = fmod(i * G[j],1);
        }

    G.clear();

    return U;
}

Dain 2007-03-12 11:04 发表评论

Dain — Wed, 10 Jan 2007 03:15:00 GMT

(t��ng) 二叉�?w��i)方法可以和Monte Carlo模拟�l�合��h��生证券定仗��二叉树(w��i)定�h(hu��n)模型是从构造好的二叉树(w��i)中随机选择一条�\径样本，从二叉树(w��i)的末端开始倒推计算�?gu��)��生证券的��h��Q�但是采用了(ji��n)Monte Carlo后，是顺着二叉�?w��i)往后计��的�?br /> (t��ng) 基本�Ҏ(gu��)��Q��?t��ng) (t��ng) (t��ng) (t��ng) (t��ng) (t��ng) (t��ng)?br /> (t��ng) 在第一个节点（根节点）(j��)�Q�随��Z�生一�?�?间的随机敎ͼ�如果�q�个数小于p�Q�就选择当前的上升分支，反之选择下降分支。这样就产生�?ji��n)一个新节点�Q��l�上面的�q�程�Q�直��C��叉树(w��i)的末端。一条�\径��生了(ji��n)�Q�衍生证券的最�l��h(hu��n)值就可以计算出来�?ji��n)（可以看作是全部可能终值集合中的一个随机样本）(j��)�Q�这样完成了(ji��n)�W�一�ơ模拟。更多的��h��路径得到更多的样本终倹{��进行多�ơ模拟，用��^均值来估计衍生证券的�h(hu��n)根{�?/font>

Dain 2007-01-10 11:15 发表评论