先說下今天寫VBA學(xué)到的，那就是Excel的統(tǒng)計(jì)工作表函數(shù)。
Excel的統(tǒng)計(jì)工作表函數(shù)用于對數(shù)據(jù)區(qū)域進(jìn)行統(tǒng)計(jì)分析。例如，統(tǒng)計(jì)工作表函數(shù)可以用來統(tǒng)計(jì)樣本的方差、數(shù)據(jù)區(qū)間的頻率分布等。是不是覺得好像是很專業(yè)范疇的東西？是的，統(tǒng)計(jì)工作表函數(shù)中提供了很多屬于統(tǒng)計(jì)學(xué)范疇的函數(shù)，但也有些函數(shù)其實(shí)在你我的日常生活中是很常用的，比如求班級平均成績，排名等。
但是我的程序是要cpp實(shí)現(xiàn)上面?zhèn)z個(gè)函數(shù)，可是cpp沒有這樣的統(tǒng)計(jì)函數(shù)。查了好多資料，找到了多項(xiàng)式近似的方法：
/***************************************************************/
/* 返回標(biāo)準(zhǔn)正態(tài)分布的累積函數(shù)，該分布的平均值為 0，標(biāo)準(zhǔn)偏差為 1。 */
/***************************************************************/
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;
}
/***************************************************************/
/* 返回標(biāo)準(zhǔn)正態(tài)分布累積函數(shù)的逆函數(shù)。該分布的平均值為 0，標(biāo)準(zhǔn)偏差為 1。 */
/***************************************************************/
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);
}
}