/usr/share/openturns/validation/ValidEstimatedTruncatedNormal.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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 | > restart:
> Phi:=proc(x)
> int(1/sqrt(2*Pi)*exp(-t^2/2),t=-infinity..x)
> end:
> sigma:=sqrt(v);
> #PhiA:=Phi((a-mu)/sigma);
> #PhiB:=Phi((b-mu)/sigma);
> #phiA:=1/sqrt(2*Pi)*exp(-((a-mu)/sigma)^2/2);
> #phiB:=1/sqrt(2*Pi)*exp(-((b-mu)/sigma)^2/2);
> assume(PhiB>PhiA,b>a,b>m,a<m);
> iDenom:=1/(PhiB-PhiA);ratio:=(phiB-phiA)*iDenom*sigma;aNorm:=(a-mu)/si
> gma;bNorm:=(b-mu)/sigma;
> eq:={m=mu-sigma^2*(phiB-phiA)/(PhiB-PhiA),s2=(sigma * sigma * (1 -
> sigma * (bNorm * phiB - aNorm * phiA) * iDenom - ratio * ratio))};
> sol:=map(factor,solve(eq,{mu,v}));
1/2
sigma := v
1
iDenom := -------------
PhiB~ - PhiA~
1/2
(phiB - phiA) v
ratio := ------------------
PhiB~ - PhiA~
a~ - mu
aNorm := -------
1/2
v
b~ - mu
bNorm := -------
1/2
v
/
|
|
|
eq := {s2 = v |
|
\
1/2 /(b~ - mu) phiB (a~ - mu) phiA\
v |-------------- - --------------|
| 1/2 1/2 | 2
\ v v / (phiB - phiA) v
1 - -------------------------------------- - ----------------
PhiB~ - PhiA~ 2
(PhiB~ - PhiA~)
\
|
|
| v (phiB - phiA)
|, m~ = mu - ---------------}
| PhiB~ - PhiA~
/
2 2
sol := {mu = (-m~ PhiA~ + phiB m~ - phiA m~ + phiA a~ m~
- phiB b~ m~ + s2 phiB - s2 phiA + m~ PhiB~)/(
-PhiA~ + phiB m~ - phiA m~ + phiA a~ - phiB b~ + PhiB~),
s2 (-PhiB~ + PhiA~)
v = - ------------------------------------------------------}
-PhiA~ + phiB m~ - phiA m~ + phiA a~ - phiB b~ + PhiB~
> factor(subs(sol,mu)-1);
2 2
(-m~ PhiA~ + phiB m~ - phiA m~ + phiA a~ m~ - phiB b~ m~
+ s2 phiB - s2 phiA + m~ PhiB~ + PhiA~ - phiB m~ + phiA m~
- phiA a~ + phiB b~ - PhiB~)/(
-PhiA~ + phiB m~ - phiA m~ + phiA a~ - phiB b~ + PhiB~)
>
|