/usr/share/openturns/validation/ValidSpecFunc.txt is in openturns-validation 1.5-7build2.
This file is owned by root:root, with mode 0o644.
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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 | > restart:
> Rfs:=(int((diff(1/sqrt(2*Pi)*exp(-x*x/2),x$2))^2,x=-infinity..infinity
> ));
> assume(x>0,x<1):
> _beta:=Beta(a,b);
> _betaInc:=int(t^(a-1)*(1-t)^(b-1),t=0..x);
> _betaRatioInc:=_betaInc/beta;
> valnum:=a=3.5,b=5.6:
> valx:=x=0.3:
> valy:=y=0.002:
> beta:=evalf(subs(valnum,_beta));
> betaInc:=evalf(subs(valnum,valx,_betaInc));
> betaRatioInc:=evalf(subs(valnum,valx,_betaRatioInc));
> betaIncInv:=fsolve(subs(valnum,_betaInc)=subs(valy,y),x,0..1);
> betaRatioIncInv:=fsolve(subs(valnum,_betaRatioInc)=subs(valy,y),x,0..1
> );
_beta := Beta(a, b)
a
x~ hypergeom([a, -b + 1], [1 + a], x~)
_betaInc := ---------------------------------------
a
a
x~ hypergeom([a, -b + 1], [1 + a], x~)
_betaRatioInc := ---------------------------------------
a beta
beta := 0.004093457689
betaInc := 0.001297399181
betaRatioInc := 0.3169445686
betaIncInv := 0.3711124504
betaRatioIncInv := 0.05322108266
>
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