/usr/share/openturns/validation/ValidGumbelEstimate.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 | > restart:
> with(Statistics):
> assume(alpha>0);
> gumbel_:=RandomVariable(Gumbel(beta,1/alpha)):
> pdf:=PDF(gumbel_,x);
> mu_:=Mean(gumbel_);
> var_:=Variance(gumbel_);
> assume(v>0):
> sol:=allvalues(solve({mu_=m,var_=v},{alpha,beta})):
> map(_x->collect(simplify(_x,symbolic),m),subs(sol[1],v=sigma^2,[alpha,
> beta]));
>
pdf := alpha~ exp(-(x - beta) alpha~) exp(-exp(-(x - beta) alpha~))
gamma
mu_ := beta + ------
alpha~
2
Pi
var_ := ---------
2
6 alpha~
1/2 1/2
6 Pi gamma sigma 6
[-------, m - ----------------]
6 sigma Pi
> map(_x->collect(simplify(_x,symbolic),m),subs(sol[1],v=sigma^2,[alpha,
> beta]));
1/2 1/2
6 Pi gamma sigma 6
[-------, m - ----------------]
6 sigma Pi
>
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