/usr/share/openturns/validation/DefaultDistribution.txt is in openturns-validation 1.5-7build2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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> a:=-1:
> b:=1:
> PhiA:=int(1/sqrt(2*Pi)*exp(-x^2/2),x=-infinity..a):
> evalf[16](PhiA);
> PhiB:=int(1/sqrt(2*Pi)*exp(-x^2/2),x=-infinity..b);
> evalf[16](PhiB);
> phiA:=1/sqrt(2*Pi)*exp(-a^2/2);
> evalf[16](phiA);
> phiB:=1/sqrt(2*Pi)*exp(-b^2/2);
> evalf[16](phiB);
> normalizationFactor:=1/(PhiB - PhiA);
> evalf[16](normalizationFactor);
> phiANorm:=phiA*normalizationFactor;
> evalf[16](phiANorm);
> phiBNorm:=phiB*normalizationFactor;
> evalf[16](phiBNorm);
> PhiANorm:=PhiA*normalizationFactor;
> evalf[16](PhiANorm);
> PhiBNorm:=PhiB*normalizationFactor;
> evalf[16](PhiBNorm);
0.1586552539314570
/ 1/2 1/2 1/2 \
1/2 |2 Pi 1/2 1/2 2 |
2 |---------- + 1/2 2 Pi erf(----)|
\ 2 2 /
PhiB := 1/2 --------------------------------------------
1/2
Pi
0.8413447460685425
1/2
2 exp(-1/2)
phiA := 1/2 --------------
1/2
Pi
0.2419707245191433
1/2
2 exp(-1/2)
phiB := 1/2 --------------
1/2
Pi
0.2419707245191433
/
|
|
|
normalizationFactor := 1/|
|
\
/ 1/2 1/2 1/2 \
1/2 |2 Pi 1/2 1/2 2 |
2 |---------- + 1/2 2 Pi erf(----)|
\ 2 2 /
1/2 --------------------------------------------
1/2
Pi
/ 1/2 1/2 1/2 \\
1/2 |2 Pi 1/2 1/2 2 ||
2 |---------- - 1/2 2 Pi erf(----)||
\ 2 2 /|
- 1/2 --------------------------------------------|
1/2 |
Pi /
1.464794773491545
/ /
| |
| |
1/2 / | 1/2 |
phiANorm := 1/2 2 exp(-1/2) / |Pi |
/ | |
\ \
/ 1/2 1/2 1/2 \
1/2 |2 Pi 1/2 1/2 2 |
2 |---------- + 1/2 2 Pi erf(----)|
\ 2 2 /
1/2 --------------------------------------------
1/2
Pi
/ 1/2 1/2 1/2 \\\
1/2 |2 Pi 1/2 1/2 2 |||
2 |---------- - 1/2 2 Pi erf(----)|||
\ 2 2 /||
- 1/2 --------------------------------------------||
1/2 ||
Pi //
0.3544374526136036
/ /
| |
| |
1/2 / | 1/2 |
phiBNorm := 1/2 2 exp(-1/2) / |Pi |
/ | |
\ \
/ 1/2 1/2 1/2 \
1/2 |2 Pi 1/2 1/2 2 |
2 |---------- + 1/2 2 Pi erf(----)|
\ 2 2 /
1/2 --------------------------------------------
1/2
Pi
/ 1/2 1/2 1/2 \\\
1/2 |2 Pi 1/2 1/2 2 |||
2 |---------- - 1/2 2 Pi erf(----)|||
\ 2 2 /||
- 1/2 --------------------------------------------||
1/2 ||
Pi //
0.3544374526136036
/
|
/ 1/2 1/2 1/2 \ |
1/2 |2 Pi 1/2 1/2 2 | / |
PhiANorm := 1/2 2 |---------- - 1/2 2 Pi erf(----)| / |
\ 2 2 / / |
\
/ / 1/2 1/2 1/2 \
| 1/2 |2 Pi 1/2 1/2 2 |
| 2 |---------- + 1/2 2 Pi erf(----)|
1/2 | \ 2 2 /
Pi |1/2 --------------------------------------------
| 1/2
\ Pi
/ 1/2 1/2 1/2 \\\
1/2 |2 Pi 1/2 1/2 2 |||
2 |---------- - 1/2 2 Pi erf(----)|||
\ 2 2 /||
- 1/2 --------------------------------------------||
1/2 ||
Pi //
0.2323973867457722
/
|
/ 1/2 1/2 1/2 \ |
1/2 |2 Pi 1/2 1/2 2 | / |
PhiBNorm := 1/2 2 |---------- + 1/2 2 Pi erf(----)| / |
\ 2 2 / / |
\
/ / 1/2 1/2 1/2 \
| 1/2 |2 Pi 1/2 1/2 2 |
| 2 |---------- + 1/2 2 Pi erf(----)|
1/2 | \ 2 2 /
Pi |1/2 --------------------------------------------
| 1/2
\ Pi
/ 1/2 1/2 1/2 \\\
1/2 |2 Pi 1/2 1/2 2 |||
2 |---------- - 1/2 2 Pi erf(----)|||
\ 2 2 /||
- 1/2 --------------------------------------------||
1/2 ||
Pi //
1.232397386745772
> evalf[20](1/(int(1/sqrt(2*Pi)*exp(-x^2/2),x=-infinity..1)-int(1/sqrt(2
> *Pi)*exp(-x^2/2),x=-infinity..-1)));
1.4647947734915440800
> evalf[20](1/(sqrt(3-2)*Beta(1/2,3/2)));
0.63661977236758134306
> evalf[20](sqrt(1/3));
0.57735026918962576449
> evalf[20](1/sqrt(2*Pi));
0.39894228040143267794
>
|