Lista 5 + Resolução (EQM, Consistência, Newton-Raphson, EMV, Informação de Fisher, Vicio, Avaliação de Estimadores)

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###Exercício 2 - lista 5 (Weibull): 
 
x<-rweibull(n=10,shape=1,scale=1) 
n<-length(x) 
 
NR<-function(a,b){ 
 theta_new<-c(a,b)- 
 solve(matrix(c(-n/a^2-
sum(x^a*(log(x))^2)*(1/b^a)+(1/b^a)*log(b)*sum(x^a*log(x))+sum(x^a*log(x))*log(b)/b^a-
1/b^a*(log(b))^2*sum(x^a), 
 -n/b+sum(x^a*log(x))*a/(b^(a+1))+sum(x^a)*(1/b^(a+1))-
sum(x^a)*(a/b^(a+1))*log(b), 
 -
n/b+sum(x^a*log(x))*a/(b^(a+1))+sum(x^a)*(b^(a+1)+a*log(b)/(b^(a+1)))/(b^(2*a+2)), 
 n/(b^2)+n*(a-1)/(b^2)+sum(x^a)*a*(-a-
1)/(b^(a+2))),ncol=2,nrow=2,byrow=T))%*%c(n/a+sum(log(x))-n*log(b)-
sum(x^a*log(x))*1/(b^a)+sum(x^a)*1/(b^a)*log(b),-n/b-n*(a-1)/b+sum(x^a)*a/(b^(a+1))) 
 theta_new 
} 
NR(1,1) 
 
eps<-0.000000001 
a_old<-1 
b_old<-1 
erro_a<-1 
erro_b<-1 
while(abs(erro_a)>eps || abs(erro_b)>eps){ 
 theta_new<-NR(a_old,b_old) 
 a_new<-theta_new[1,1] 
 b_new<-theta_new[2,1] 
 erro_a<-a_new-a_old 
 erro_b<-b_new-b_old 
 a_old<-a_new 
 b_old<-b_new 
 print(c(a_new,b_new)) 
}