Participation<-c(67.5,65.6,65.7,59.3,39.8,76.1,73.6,81.6,75.5,80.3,54.5,79.1,94,80.3,89.6,44.7,82.7,89.7,83.6,84.9,76.3,74.7,68.8,79.3)

Diff<-c(13,19,18,12,20,5,1,1,2,3,6,5,4,8,1,3,18,13,2,2,12,17,26,6)

B<-1000
Bcors<-NULL
for (i in 1:B){
k<-sample(1:24,replace=TRUE)
rele<-electionsUS[k,]
Bcors<-c(Bcors,cor(rele[,1],rele[,2]))
}


Bcorss<-sort(Bcors)



xi<-(Bcors-cor(Participation,Diff))/sqrt(var(Bcors))

round(c(cor(Participation,Diff)-xis[975]*sqrt(var(Bcors)),cor(Participation,Diff)-xis[25]*sqrt(var(Bcors))),4)




sum(Bcors<cor(Participation,Diff))
b0<-qnorm(0.527,0,1)


p1<-pnorm(qnorm(0.025,0,1)+2*b0,0,1)

p2<-pnorm(qnorm(0.975,0,1)+2*b0,0,1)


####### Παράδειγμα accidents ######

accs<-c(1,2,5,0,3,1,0,1,1,2,0,1,8,0,5,0,2,1,2,3)
I<-var(accs)/mean(accs)

B<-1000
bI<-NULL
for (i in 1:B){
bsample<-sample(accs,replace=TRUE)
bI<-c(var(bsample)/mean(bsample),bI)
}

##### Απλό bootstrap δ.ε. 

c(I-qnorm(0.975,0,1)*sqrt(var(bI)),I-qnorm(0.025,0,1)*sqrt(var(bI)))


##### Ποσοστιαίο bootstrap δ.ε. 

c(sort_bI[25],sort_bI[975])

xi<-(bI-I)/sqrt(var(bI))


##### t-Ποσοστιαίο bootstrap δ.ε. 

c(I-xi_sort[975]*sqrt(var(bI)),I-xi_sort[25]*sqrt(var(bI)))


#######  BCa δ.ε. για το I 

b0<-qnorm(0.559,0,1)

p1<-pnorm(qnorm(0.025)+2*b0)

p2<-pnorm(qnorm(0.975)+2*b0)

c(sort_bI[48],sort_bI[988])