/usr/share/openturns/validation/ValidExponential.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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> with(Statistics):
> exponential_:=RandomVariable(Exponential(1/lambda)):
> assume(u>0);
> pdf:=subs(u=x-_gamma,PDF(exponential_,u));
> ddf:=diff(pdf,x);
> cdf:=subs(u=x-_gamma,CDF(exponential_,u));
> cf:=subs(u=x,exp(-I*_gamma)*CharacteristicFunction(exponential_,u));
> mu_:=_gamma+Mean(exponential_);
> var_:=Variance(exponential_);
> skew_:=simplify(convert(Skewness(exponential_),GAMMA),symbolic);
> kurt_:=simplify(convert(Kurtosis(exponential_),GAMMA),symbolic);
> qdf:=_gamma+Quantile(exponential_,p);
> qdf2:=solve(cdf=p,x);
> pdfgr:=[factor(diff(pdf,lambda)),factor(diff(pdf,_gamma))];
> cdfgr:=[factor(diff(cdf,lambda)),factor(diff(cdf,_gamma))];
> valnum:=lambda=2.5,_gamma=-0.5:
> evalf(subs(valnum,x=1,ddf));
> evalf(subs(valnum,x=1,pdf));
> evalf(subs(valnum,x=1,cdf));
> evalf(subs(valnum,x=1,cf));
> evalf(subs(valnum,x=1,map(_x->_x,pdfgr)));
> evalf(subs(valnum,x=1,cdfgr));
> evalf(solve(subs(valnum,cdf)=0.95,x));
> evalf(subs(valnum,mu_));
> evalf(subs(valnum,sqrt(var_)));
> evalf(subs(valnum,skew_));
> evalf(subs(valnum,kurt_));
> evalf(subs(valnum,var_));
pdf := lambda exp(-(x - _gamma) lambda)
2
ddf := -lambda exp(-(x - _gamma) lambda)
cdf := 1 - exp(-(x - _gamma) lambda)
exp(-I _gamma)
cf := --------------
x I
1 - ------
lambda
1
mu_ := _gamma + ------
lambda
1
var_ := -------
2
lambda
skew_ := 2
kurt_ := 9
ln(1 - p)
qdf := _gamma - ---------
lambda
lambda _gamma - ln(1 - p)
qdf2 := -------------------------
lambda
pdfgr := [
-exp(-(x - _gamma) lambda) (-1 + lambda x - lambda _gamma),
2
lambda exp(-(x - _gamma) lambda)]
cdfgr := [(x - _gamma) exp(-(x - _gamma) lambda),
-lambda exp(-(x - _gamma) lambda)]
-0.1469859116
0.05879436465
0.9764822541
0.5912175400 + 0.7159125546 I
[-0.06467380112, 0.1469859116]
[0.03527661879, -0.05879436465]
0.6982929094
-0.1000000000
0.4000000000
2.
9.
0.1600000000
>
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