######################################################################################## ## This code is for learning normal distribution ## [EMS] Chapter 5 ## created on Jan. 05, 2007 by Leena Choi ## modified on Jan. 13, 2007 by Leena Choi ######################################################################################## ######################################################################################## ## normal distributions and standard normal distributions ######################################################################################## #library(grDevices) ## normal distribution with mean=mu and sd=sigma set.seed(191) mu <- 171.5 sigma <- 6.5 height <- rnorm(500, mean=mu, sd=sigma) dd <- density(height, adjust = 1.5,) yrange <- range(dd\$y) hist(height, probability = T, nclass=20, axes=F, ylim=c(0.0025, 0.07), ylab=" ", xlab="Height", main="Distribution of Height") lines(dd\$x, dd\$y, col=2, lwd=2) abline(v=0, lty=1, col=4, lwd=2) text(182, 0.053, "Normal density curve", col=2) axis(1) par(mfrow=c(1,1)) x <- seq(150, 195, by=0.5) y <- dnorm(x, mean=mu, sd=sigma) plot(x, y, lwd=2, xlim=c(148, 198), ylim=c(0.0025, 0.07), col=2, type="l", xlab="Height (cm)", ylab="Density", bty="n") text(mu, 0.066, labels = paste("\m =",mu), pos=1, vfont=c("serif symbol", "plain"), cex=1.2, col=3) abline(v=mu, col=3, lty=2, lwd=1) ## convert to z-score z <- (x - mu)/sigma plot(z, y, lwd=2, xlim=c(-4, 4), ylim=c(0.0025, 0.07), col=2, type="l", xlab="z-score", ylab="Density", bty="n") text(0, 0.066, labels = paste("\m =",0), pos=1, vfont=c("serif symbol", "plain"), cex=1.2, col=3) abline(v=0, col=3, lty=2, lwd=1) ## comparison par(mfrow=c(2,1)) plot(x, y, lwd=2, xlim=c(148, 198), ylim=c(0.0025, 0.07), col=2, type="l", xlab="Height (cm)", ylab="Density", bty="n") text(mu, 0.075, labels = paste("\m =",mu), pos=1, vfont=c("serif symbol", "plain"), cex=1.2, col=3) abline(v=mu, col=3, lty=2, lwd=1) plot(z, y, lwd=2, xlim=c(-4, 4), ylim=c(0.0025, 0.07), col=2, type="l", xlab="z-score", ylab="Density", bty="n") text(0, 0.075, labels = paste("\m =",0), pos=1, vfont=c("serif symbol", "plain"), cex=1.2, col=3) abline(v=0, col=3, lty=2, lwd=1) ## z-score ; Standard normal deviate (SND) par(mfrow=c(1,1)) plot(z, y, lwd=2, xlim=c(-4, 4), ylim=c(0.0025, 0.07), col=2, type="l", xlab="z-score", ylab="Density", bty="n") abline(v=0, col=3, lty=2, lwd=1) text(0.1, 0.065, labels = paste("\m =",0), vfont=c("serif symbol", "plain"), cex=1.2, col=3) u.1s <- 1 l.1s <- -1 segments(u.1s, -0.002, u.1s, 0.0365, col=6, lwd=1) segments(l.1s, -0.002, l.1s, 0.0365, col=6, lwd=1) text(1, 0.043, labels = paste("+1","\s", sep=""), pos=4, vfont=c("serif symbol", "plain"), cex=1, col=6) text(-1, 0.043, labels = paste("-1","\s", sep=""), pos=2, vfont=c("serif symbol", "plain"), cex=1, col=6) u.2s <- 2 l.2s <- -2 segments(u.2s, -0.002, u.2s, 0.0082, col=5, lwd=1) segments(l.2s, -0.002, l.2s, 0.0082, col=5, lwd=1) text(2, 0.009, labels = paste("+2","\s", sep=""), pos=4, vfont=c("serif symbol", "plain"), cex=1, col=5) text(-2, 0.009, labels = paste("-2","\s", sep=""), pos=2, vfont=c("serif symbol", "plain"), cex=1, col=5) u.3s <- 3 l.3s <- -3 segments(u.3s, -0.002, u.3s, 0.0006, col=4, lwd=2) segments(l.3s, -0.002, l.3s, 0.0006, col=4, lwd=2) text(3, 0.002, labels = paste("+3","\s", sep=""), pos=4, vfont=c("serif symbol", "plain"), cex=1, col=4) text(-3, 0.002, labels = paste("-3","\s", sep=""), pos=2, vfont=c("serif symbol", "plain"), cex=1, col=4) ## Density Curve par(mfrow=c(1,1)) plot(x, y, lwd=2, xlim=c(148, 198), ylim=c(0.0025, 0.07), col=2, type="l", xlab="Height (cm)", ylab="Density", bty="n") abline(v=mu, col=3, lty=2, lwd=1) text(mu+3, 0.065, labels = paste("\m =",mu), vfont=c("serif symbol", "plain"), cex=1.2, col=3) u.1s <- mu + sigma l.1s <- mu - sigma segments(u.1s, -0.002, u.1s, 0.0365, col=6, lwd=1) segments(l.1s, -0.002, l.1s, 0.0365, col=6, lwd=1) text(180, 0.043, labels = paste("\\+-1s"), vfont=c("serif symbol", "plain"), cex=1, col=6) u.2s <- mu + 2*sigma l.2s <- mu - 2*sigma segments(u.2s, -0.002, u.2s, 0.0082, col=5, lwd=1) segments(l.2s, -0.002, l.2s, 0.0082, col=5, lwd=1) text(187, 0.009, labels = paste("\\+-2s"), vfont=c("serif symbol", "plain"), cex=1, col=5) u.3s <- mu + 3*sigma l.3s <- mu - 3*sigma segments(u.3s, -0.002, u.3s, 0.0006, col=4, lwd=2) segments(l.3s, -0.002, l.3s, 0.0006, col=4, lwd=2) text(194, 0.002, labels = paste("\\+-3s"), vfont=c("serif symbol", "plain"), cex=1, col=4)