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

Lorentz JÄNTSCHI (principal investigator) & Sorana D. BOLBOACĂ (co-investigator)
CIWilson_C(X,m) =
2
z 1
X + ±
2 2
2
m + z
± z
38(157)
z
2
−
4
1
m
⎛ X −1
⎞
+ X⎜1−
⎟ ±
⎝ m ⎠
÷ Algoritmi de calcul:
function Wilson_N(){
tX = this->X + this->z2/2.0; tn = this->n + this->z2;
t0 = this->z * pow(Wald_0+this->z2/4.0,0.5);
this->Xi = (tX-t0)/tn; this->Xs = (tX+t0)/tn;
}
function Wilson_C(){
t0 = 2.0*this->X+this->z2;t1 = 2.0*(this->n+this->z2);
t2 = this->z2-1.0/this->n;
this->Xi = (this->X==0 ? 0 :
(t0-this->z*pow(t2+4*this->X*(1-(this->X-1)/this->n)-2,0.5)-1)/t1);
this->Xs = (this->X==this->n ? 1 :
(t0+this->z*pow(t2+4*this->X*(1-(this->X+1)/this->n)+2,0.5)+1)/t1);
}
÷ Formule matematice:
Intervalul de încredere Agresti-Coull
CIA_C__N(X,m) = CIWald_N(X+z 2 /2,m+z 2 )
CIA_C__C(X,m) = CIWald_N(X+z 2 /4,m+z 2 /2)
CIA_C__D(X,m) = CIWald_N(X+1+4X(m-X)/m,m+4)
÷ Algoritmi de calcul:
function A_C__N(){
this->Wald_1(this->X+this->z2/2,this->n+this->z2);
}
function A_C__C(){
this->Wald_1(this->X+this->z2/4,this->n+this->z2/2);
}
function A_C__D(){
t = Wald_0/this->n;
Wald_1(this->X+1+4*t,this->n+4);
}
÷ Formule matematice:
Intervalul de încredere ArcSine
CIArcS_N(X,m) = sin 2 (arcsin(√(X/m)±z/√(4n))
CIArcS_C(X,m) = sin 2 (arcsin(√((X+3/8)/(m+3/4))±z/√(4n))
CIArcS_D(X,m) = sin 2 (arcsin(√((X±1/2)/m)±z/√(4n))
CIArcS_E(X,m) = CIArcS_C(X,m) = sin 2 (arcsin(√((X+3/8±1/2)/(m+3/4))±z/√(4n))
÷ Algoritmi de calcul:
function ArcS_N(){
tX = asin(pow(this->X_n,0.5));
t0 = this->z/pow(4*this->n,0.5);
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