| 7 |
|
|
| 8 |
|
relies on gauss.cal and norm.cal |
| 9 |
|
} |
| 10 |
+ |
|
| 11 |
|
Z1(u) = Z((u - mean1)/stdev1) / stdev1; |
| 12 |
|
Z2(u) = Z((u - mean2)/stdev2) / stdev2; |
| 13 |
|
|
| 15 |
|
|
| 16 |
|
xmin = min(mean1-3*stdev1, mean2-3*stdev2); |
| 17 |
|
xmax = max(mean1+3*stdev1, mean2+3*stdev2); |
| 18 |
+ |
|
| 19 |
+ |
{ |
| 20 |
+ |
Following is an alternative calculation that doesn't |
| 21 |
+ |
require numerical integration, nor gauss.cal nor norm.cal |
| 22 |
+ |
|
| 23 |
+ |
(ref: stats.stackexchange.com/questions/103800 – wolfies Dec 24 '16 at 14:40) |
| 24 |
+ |
} |
| 25 |
+ |
|
| 26 |
+ |
abs(x) : if(x, x, -x); |
| 27 |
+ |
|
| 28 |
+ |
Finteg(c, m, s) : 0.5*erf((c-m)/(sqrt(2)*s)); |
| 29 |
+ |
|
| 30 |
+ |
m1 = mean1; m2 = mean2; |
| 31 |
+ |
s1 = stdev1; s2 = stdev2; |
| 32 |
+ |
|
| 33 |
+ |
den = s1*s1 - s2*s2; |
| 34 |
+ |
c0 = (m2*s1*s1 - m1*s2*s2)/den; |
| 35 |
+ |
cr = s1*s2*sqrt((m1-m2)*(m1-m2) + 2*den*log(s1/s2))/den; |
| 36 |
+ |
|
| 37 |
+ |
NormOverlap = if(1e-7 - abs(s1-s2), 1 - erf(abs(m1-m2)/(s1+s2)/sqrt(2)), |
| 38 |
+ |
1 - Finteg(c0-cr,m1,s1) + Finteg(c0-cr,m2,s2) |
| 39 |
+ |
+ Finteg(c0+cr,m1,s1) - Finteg(c0+cr,m2,s2) ); |
