#Distribuciķ Normal #Evoluciķ de l'amplada de l'interval de confianįa per a la Mitjana de la poblaciķ #a mesura que incrementa n i per diferents alfas. Varāncia poblacional DESconeguda #Fixem la llavor per a que l'experiment sempre surti el mateix set.seed(1000) #Fiquem les dades rep<-500 nvars<-seq(2,100,1) mu<-10 sigma<-3 #Creem els vectors necessaris de la Mitjana Mostral e_mu0.hat<-vector() eII_mu0.hat<-vector() eIS_mu0.hat<-vector() e2_mu0.hat<-vector() eII2_mu0.hat<-vector() eIS2_mu0.hat<-vector() e_mu1.hat<-vector() eII_mu1.hat<-vector() eIS_mu1.hat<-vector() e2_mu1.hat<-vector() eII2_mu1.hat<-vector() eIS2_mu1.hat<-vector() e_mu2.hat<-vector() eII_mu2.hat<-vector() eIS_mu2.hat<-vector() e2_mu2.hat<-vector() eII2_mu2.hat<-vector() eIS2_mu2.hat<-vector() for (i in 1:length(nvars)){ matriu.x<-matrix(rnorm(rep*nvars[i],mu,sigma),rep) #Interval alfa alfa=0.1 mu0.hat<-rowMeans(matriu.x) matriu.xc<-(matriu.x-mu0.hat)^2 sd0.hat<-sqrt(rowSums(matriu.xc)/(nvars[i]-1)) II_mu0.hat<-mu0.hat+qt(alfa/2,nvars[i]-1)*sd0.hat/sqrt(nvars[i]) IS_mu0.hat<-mu0.hat+qt(1-alfa/2,nvars[i]-1)*sd0.hat/sqrt(nvars[i]) e_mu0.hat[i]<-mean(mu0.hat) eII_mu0.hat[i]<-mean(II_mu0.hat) eIS_mu0.hat[i]<-mean(IS_mu0.hat) e2_mu0.hat<-rbind(e2_mu0.hat,e_mu0.hat[i]) eII2_mu0.hat<-rbind(eII2_mu0.hat,eII_mu0.hat[i]) eIS2_mu0.hat<-rbind(eIS2_mu0.hat,eIS_mu0.hat[i]) alfa=0.05 mu1.hat<-rowMeans(matriu.x) matriu.xc<-(matriu.x-mu1.hat)^2 sd1.hat<-sqrt(rowSums(matriu.xc)/(nvars[i]-1)) II_mu1.hat<-mu1.hat+qt(alfa/2,nvars[i]-1)*sd1.hat/sqrt(nvars[i]) IS_mu1.hat<-mu1.hat+qt(1-alfa/2,nvars[i]-1)*sd1.hat/sqrt(nvars[i]) e_mu1.hat[i]<-mean(mu1.hat) eII_mu1.hat[i]<-mean(II_mu1.hat) eIS_mu1.hat[i]<-mean(IS_mu1.hat) e2_mu1.hat<-rbind(e2_mu1.hat,e_mu1.hat[i]) eII2_mu1.hat<-rbind(eII2_mu1.hat,eII_mu1.hat[i]) eIS2_mu1.hat<-rbind(eIS2_mu1.hat,eIS_mu1.hat[i]) alfa=0.01 mu2.hat<-rowMeans(matriu.x) matriu.xc<-(matriu.x-mu2.hat)^2 sd2.hat<-sqrt(rowSums(matriu.xc)/(nvars[i]-1)) II_mu2.hat<-mu2.hat+qt(alfa/2,nvars[i]-1)*sd2.hat/sqrt(nvars[i]) IS_mu2.hat<-mu2.hat+qt(1-alfa/2,nvars[i]-1)*sd2.hat/sqrt(nvars[i]) e_mu2.hat[i]<-mean(mu2.hat) eII_mu2.hat[i]<-mean(II_mu2.hat) eIS_mu2.hat[i]<-mean(IS_mu2.hat) e2_mu2.hat<-rbind(e2_mu2.hat,e_mu2.hat[i]) eII2_mu2.hat<-rbind(eII2_mu2.hat,eII_mu2.hat[i]) eIS2_mu2.hat<-rbind(eIS2_mu2.hat,eIS_mu2.hat[i]) } res0<-cbind(e2_mu0.hat,eII2_mu0.hat,eIS2_mu0.hat) res1<-cbind(e2_mu1.hat,eII2_mu1.hat,eIS2_mu1.hat) res2<-cbind(e2_mu2.hat,eII2_mu2.hat,eIS2_mu2.hat) nomscol<-c("Esperanįa", "I. Inferior", "I. Superior") colnames(res0)<-nomscol colnames(res1)<-nomscol colnames(res2)<-nomscol res0; res1; res2; #Anālisi grāfica. #Generem una matriu grāfica d'una fila i dues columnes par(mfrow = c(1,3), oma=c(1, 0, 4, 0)) #Grāfic a la posiciķ 1,1 y<-seq(mu-2.5*sigma, mu+2.5*sigma, along=nvars) x<-nvars plot(x,y, main='Alfa=0.1',xlab = "Mida mostral", ylab = "", type="n") abline(h=mu) lines(x,e2_mu0.hat, lty=1, lwd=3, col='red') lines(x,eII2_mu0.hat, lty=1, lwd=3, col='blue') lines(x,eIS2_mu0.hat, lty=1, lwd=3, col='blue') #Grāfic a la posiciķ 1,2 y<-seq(mu-2.5*sigma, mu+2.5*sigma, along=nvars) x<-nvars plot(x,y, main='Alfa=0.05',xlab = "Mida mostral", ylab = "", type="n") abline(h=mu) lines(x,e2_mu1.hat, lty=1, lwd=3, col='red') lines(x,eII2_mu1.hat, lty=1, lwd=3, col='blue') lines(x,eIS2_mu1.hat, lty=1, lwd=3, col='blue') #Grāfic a la posiciķ 1,3 y<-seq(mu-2.5*sigma, mu+2.5*sigma, along=nvars) x<-nvars plot(x,y, main='Alfa=0.01',xlab = "Mida mostral", ylab = "", type="n") abline(h=mu) lines(x,e2_mu2.hat, lty=1, lwd=3, col='red') lines(x,eII2_mu2.hat, lty=1, lwd=3, col='blue') lines(x,eIS2_mu2.hat, lty=1, lwd=3, col='blue') mtext(side=3, line=0, cex=1.5, outer=T,"Interval de confianįa per a la Mitjana Poblacional. Variāncia DESconeguda.") mtext(side=1, line=-1, cex=0.75, outer=T, adj=1, "Script creat per Jordi Lķpez-Tamayo ")