#Jordi López-Tamayo, Gener 2011
#Relació entre la distribució de la mitjana mostral 
#i la població a mesura que incrementa la mida mostral

mu_p <- 0 ; 
mu_m <- 0 ; 
sigma_p <- 1;
IInf <- -0.25
ISup <- 0.25
Text_I <-paste("[",IInf,",",ISup,"]")


# Generació del grŕfic

par(mfrow=c(2,2), oma=c(0, 0, 4, 0))

nobs<-2
sigma_m <- sigma_p/sqrt(nobs); 
eix <- c(mu_m - 3 * sigma_p, mu_m + 3 * sigma_p)
x <- seq(eix[1], eix[2], length = 1001)
y <- dnorm(x, mu_m, sigma_m)
plot(x, y, type='l', xlab = expression(italic(n==2)), ylab = expression(italic(Densitat)), col='red', lwd=2)
abline(h = 0)
x1 <- x[x >= IInf &  x<= ISup] ; y1 <- dnorm(x1, mu_m, sigma_m)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'red')
lines(x,dnorm(x, mu_p, sigma_p), col='blue', lty=1, lwd=2)
abline(v = mu_p, col='yellow', lwd=2)
abline(v = mu_m, col='green', lwd=2)
legend("topleft", c("Població", "Mitjana Mostral"), col=c("blue","red"), lwd=2, bty="n")
#Afegim Text
pr<-pnorm(ISup, mu_m, sigma_m)-pnorm(IInf, mu_m, sigma_m)
text(mu_m+2*sigma_p, 0.75*dnorm(mu_m, mu_m, sigma_m), Text_I)
text(mu_m+2*sigma_p, 0.66*dnorm(mu_m, mu_m, sigma_m), round(pr, digits=3))

nobs<-10
sigma_m <- sigma_p/sqrt(nobs); 
eix <- c(mu_m - 3 * sigma_p, mu_m + 3 * sigma_p)
x <- seq(eix[1], eix[2], length = 1001)
y <- dnorm(x, mu_m, sigma_m)
plot(x, y, type='l', xlab = expression(italic(n==10)), ylab = expression(italic(Densitat)), col='red', lwd=2)
abline(h = 0)
x1 <- x[x >= IInf &  x<= ISup] ; y1 <- dnorm(x1, mu_m, sigma_m)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'red')
lines(x,dnorm(x, mu_p, sigma_p), col='blue', lty=1, lwd=2)
abline(v = mu_p, col='yellow', lwd=2)
abline(v = mu_m, col='green', lwd=2)
legend("topleft", c("Població", "Mitjana Mostral"), col=c("blue","red"), lwd=2, bty="n")
#Afegim Text
pr<-pnorm(ISup, mu_m, sigma_m)-pnorm(IInf, mu_m, sigma_m)
text(mu_m+2*sigma_p, 0.75*dnorm(mu_m, mu_m, sigma_m), Text_I)
text(mu_m+2*sigma_p, 0.66*dnorm(mu_m, mu_m, sigma_m), round(pr, digits=3))

nobs<-30
sigma_m <- sigma_p/sqrt(nobs); 
eix <- c(mu_m - 3 * sigma_p, mu_m + 3 * sigma_p)
x <- seq(eix[1], eix[2], length = 1001)
y <- dnorm(x, mu_m, sigma_m)
plot(x, y, type='l', xlab = expression(italic(n==30)), ylab = expression(italic(Densitat)), col='red', lwd=2)
abline(h = 0)
x1 <- x[x >= IInf &  x<= ISup] ; y1 <- dnorm(x1, mu_m, sigma_m)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'red')
lines(x,dnorm(x, mu_p, sigma_p), col='blue', lty=1, lwd=2)
abline(v = mu_p, col='yellow', lwd=2)
abline(v = mu_m, col='green', lwd=2)
legend("topleft", c("Població", "Mitjana Mostral"), col=c("blue","red"), lwd=2, bty="n")
#Afegim Text
pr<-pnorm(ISup, mu_m, sigma_m)-pnorm(IInf, mu_m, sigma_m)
text(mu_m+2*sigma_p, 0.75*dnorm(mu_m, mu_m, sigma_m), Text_I)
text(mu_m+2*sigma_p, 0.66*dnorm(mu_m, mu_m, sigma_m), round(pr, digits=3))

nobs<-60
sigma_m <- sigma_p/sqrt(nobs); 
eix <- c(mu_m - 3 * sigma_p, mu_m + 3 * sigma_p)
x <- seq(eix[1], eix[2], length = 1001)
y <- dnorm(x, mu_m, sigma_m)
plot(x, y, type='l', xlab = expression(italic(n==60)), ylab = expression(italic(Densitat)), col='red', lwd=2)
abline(h = 0)
x1 <- x[x >= IInf &  x<= ISup] ; y1 <- dnorm(x1, mu_m, sigma_m)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'red')
lines(x,dnorm(x, mu_p, sigma_p), col='blue', lty=1, lwd=2)
abline(v = mu_p, col='yellow', lwd=2)
abline(v = mu_m, col='green', lwd=2)
legend("topleft", c("Població", "Mitjana Mostral"), col=c("blue","red"), lwd=2, bty="n")
#Afegim Text
pr<-pnorm(ISup, mu_m, sigma_m)-pnorm(IInf, mu_m, sigma_m)
text(mu_m+2*sigma_p, 0.75*dnorm(mu_m, mu_m, sigma_m), Text_I)
text(mu_m+2*sigma_p, 0.66*dnorm(mu_m, mu_m, sigma_m), round(pr, digits=3))

mtext(side=3, line=0, cex=1.5, outer=T,"Relació entre la distribució de la població, la de la mitjana mostral i la mida mostral")
mtext(side=1, line=-2, cex=0.75, outer=T, adj=1, "Script creat per Jordi López-Tamayo")