/usr/share/openturns/validation/ValidEstimateLogistic.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):
> assume(beta>0):
> logistic_:=RandomVariable(Logistic(alpha,beta)):
> pdf:=PDF(logistic_,x);
> ddf:=factor(diff(pdf,x));
> cdf:=CDF(logistic_,x);
> mu_:=Mean(logistic_);
> var_:=Variance(logistic_);
> qdf:=Quantile(logistic_,p);
> qdf2:=solve(cdf=p,x);
> pdfgr:=map(factor,[diff(pdf,alpha),diff(pdf,beta)]);
> factor(pdfgr[2]-(x-alpha)*pdfgr[1]/beta);
> cdfgr:=map(factor,[diff(cdf,alpha),diff(cdf,beta)]);
> factor(dcdf[2]/dcdf[1]);
> valnum:=alpha=-0.5,beta=1.5:
> evalf(subs(valnum,x=1,ddf));
> evalf(subs(valnum,x=1,pdf));
> evalf(subs(valnum,x=1,cdf));
> 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,var_));
> evalf(subs(valnum,[mu_,sqrt(var_)]));
x - alpha
exp(---------)
beta~
pdf := ---------------------------
/ x - alpha \2
beta~ |1 + exp(---------)|
\ beta~ /
x - alpha / x - alpha \
exp(---------) |-1 + exp(---------)|
beta~ \ beta~ /
ddf := - ------------------------------------
2 / x - alpha \3
beta~ |1 + exp(---------)|
\ beta~ /
1
cdf := --------------------
x - alpha
1 + exp(- ---------)
beta~
mu_ := alpha
2 2
beta~ Pi
var_ := ----------
3
p
qdf := alpha + beta~ ln(-----)
1 - p
-1 + p
qdf2 := alpha - ln(- ------) beta~
p
x - alpha / x - alpha \
exp(---------) |-1 + exp(---------)|
beta~ \ beta~ / x - alpha /
pdfgr := [------------------------------------, exp(---------) |-x
2 / x - alpha \3 beta~ \
beta~ |1 + exp(---------)|
\ beta~ /
x - alpha x - alpha
+ x exp(---------) + alpha - alpha exp(---------) - beta~
beta~ beta~
x - alpha \ / / 3 / x - alpha \3\
- beta~ exp(---------)| / |beta~ |1 + exp(---------)| |]
beta~ / / \ \ beta~ / /
x - alpha
exp(---------)
beta~
- ----------------------------
2 / x - alpha \2
beta~ |1 + exp(---------)|
\ beta~ /
x - alpha
exp(- ---------)
beta~
cdfgr := [- -----------------------------,
/ x - alpha \2
|1 + exp(- ---------)| beta~
\ beta~ /
x - alpha
(x - alpha) exp(- ---------)
beta~
- ------------------------------]
/ x - alpha \2 2
|1 + exp(- ---------)| beta~
\ beta~ /
dcdf[2]
-------
dcdf[1]
-0.04038122117
0.1310746222
0.7310585787
[0.04038122117, -0.04700186026]
[-0.1310746222, -0.1310746222]
3.916658468
-0.5
7.402203303
[-0.5, 2.720699048]
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