Distribuţia Binomială: Modelare Statistică, Optimizare Numerică, cu ...

Lorentz JÄNTSCHI (principal investigator) & Sorana D. BOLBOACĂ (co-investigator)
this->Xi = t0-t1;
this->Xs = t0+t1;
this->Xi = (this->X==0 ? 0 : exp(this->Xi)/(1+exp(this-
>Xi)));
this->Xs = (this->X==this->n ? 1 :
exp(this->Xs)/(1+exp(this->Xs)));
}
Intervalele de încredere cu aproximaţie la binomială
÷ Formule matematice:
CIBetaC(X,m,·,c1,c2) = (Xi,Xs), unde Xi şi Xs sunt date de:
Xi
α/2 = ∫ P Beta ( t,
X + c1,
m − X + c2)
dt , 1-α/2 = ∫ P Beta ( t,
X + c2,
m − X + c1)
dt
0
CIBetaC00(X,m) = CIBetaC(X,m,0,0,0)
CIBetaC10(X,m) = CIBetaC(X,m,0,1,0)
CIBetaC01(X,m) = CIBetaC(X,m,0,0,1)
CIBetaC11(X,m) = CIBetaC(X,m,0,1,1)
CIBetaCJ0(X,m) = CIBetaC(X,m,0,0.5,0.5)
CIBetaCJ1(X,m) = CIBetaC(X,m,0,1-√(X(m-X)/m 2 ),1-√(X(m-X)/m 2 ))
CIBetaCJ2(X,m) = CIBetaC(X,m,0,0.5+√(X(m-X)/m 2 ),0.5+√(X(m-X)/m 2 ))
CIBetaCJA(X,m) = CIBetaC(X,m,0,√c1BetaCJ1c1BetaCJ2, √c2BetaCJ1c2BetaCJ2)
÷ Algoritmi de calcul:
this->a2=a/2.0; this->a21=1.0-this->a2;
this->Beta_0 = pow(Wald_0/$this->n,0.5);
function BetaC(&Xi,&Xs,X,n,c0,c1,c2){
if((X==0)||(X==n)) {
if(c0==0){
if(X){
Xi = pow(this->a,1/(n));
Xs = 1;
return;
}
if(n-X){
Xi = 0;
Xs = 1-pow(this->a,1/(n));
return;
}
}elseif(c0==1){
if(X){
Xi = pow(this->a,1/(n+1));
Xs = 1;
return;
}
if(n-X){
Xi = 0;
Xs = 1-pow(this->a,1/(n+1));
return;
}
40(157)
Xs
0