http://upload.wikimedia.org/wikipedia/commons/d/d7/Tail_Function_Graph.pdf

gaussian tail 近似式 は 1/(x*sqrt(2*pi))*exp(-x*x/2))

Gaussianとは1/sigma*sqrt(2*pi)*exp{-x*x/(2*sigma*sigma)}

erfc=1-erf(x)
erf(x) = 2/sqrt(pi)* integral from 0 to x of exp(-t*t) dt
だからgaus分布に使うときは
Prob(>x)=2.*erf(x/sqrt(2))と使わなくてはならない。
============================================-
erfc.cxx program
#include <iostream>
#include <math.h>

int main()
{
for (int i=0; i<30; i++) {
//for (double x=0.;x<6.; x+=0.1){
double x=i*0.5;
double y=0.5*erfc(x/sqrt(2.));
double xx=x;
double yy=1./(xx*sqrt(2.*3.141592))*exp(-xx*xx/2.);
for (int j=0; j<1000000; j++){
xx=j*0.0001;
//double y1=1./(xx*sqrt(2.*3.141592))*exp(-xx*xx/2.);
double y1=0.5*erfc(xx/sqrt(2.));
if(y1<y) break;
}
std::cout<<x<<" "<<y<<" "<<yy<<" :y->x "<<xx<<std::endl;
}
        return 0;
}

-------------------------------------------
$ ./a.exe
0 0.5 inf  y->x:0.0001
0.5 0.308538 0.704131  y->x:0.5001
1 0.158655 0.241971  y->x:1.0001
1.5 0.0668072 0.0863451  y->x:1.5001
2 0.0227501 0.0269955  y->x:2.0001
2.5 0.00620967 0.00701132  y->x:2.5001
3 0.0013499 0.00147728  y->x:3.0001
3.5 0.000232629 0.000249338  y->x:3.5001
4 3.16712e-05 3.34576e-05  y->x:4.0001
4.5 3.39767e-06 3.55194e-06  y->x:4.5001
5 2.86652e-07 2.97344e-07  y->x:5.0001
5.5 1.89896e-08 1.95814e-08  y->x:5.5001
6 9.86588e-10 1.01265e-09  y->x:6.0001
6.5 4.016e-11 4.10701e-11  y->x:6.5001
7 1.27981e-12 1.30496e-12  y->x:7.0001
7.5 3.19089e-14 3.24576e-14  y->x:7.5001
8 6.22096e-16 6.31534e-16  y->x:8.0001
8.5 9.47953e-18 9.60734e-18  y->x:8.5001
9 1.12859e-19 1.1422e-19  y->x:9.0001
9.5 1.04945e-21 1.06084e-21  y->x:9.5001
10 7.61985e-24 7.6946e-24  y->x:10.0001
10.5 4.31901e-26 4.3575e-26  y->x:10.5001
11 1.91066e-28 1.9262e-28  y->x:11.0001
11.5 6.59577e-31 6.64492e-31  y->x:11.5001
12 1.77648e-33 1.78865e-33  y->x:12.0001
12.5 3.73256e-36 3.75616e-36  y->x:12.5001
13 6.11716e-39 6.15295e-39  y->x:13.0001
13.5 7.81881e-42 7.86125e-42  y->x:13.5001
14 7.79354e-45 7.8329e-45  y->x:14.0001
14.5 6.05749e-48 6.08604e-48  y->x:14.5001