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## This code is for distribution shape
## [EMS] Chapter 3 on page 20-21 
## created on Jan. 05, 2007 by Leena Choi
## modified on Jan. 13, 2007 by Leena Choi
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## Distribution Shape on page 20-21 
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## Symmetrical and Bell-shaped
set.seed(191)
n <- 636
age <- rnorm(636, 9, 0.7)
yes <- c(rep(1, 145), rep(0, 491))
y <- rnorm(636, 0, 1)
dd <- density(y, adjust = 1.5,)

hist(y, probability = T, nclass=20, axes=F, ylab=" ", xlab="", main="Symmetrical\n Bell-shaped")
lines(dd$x, dd$y, col=2, lwd=2)
abline(v=0, lty=1, col=4, lwd=2)
text(2, 0.3, "Density curve", col=2)

## Positively Skewed or Skewed to the right
set.seed(191)
n <- 1000
age <- rnorm(n, 9, 0.7)
y <- 0.6+ 0.1*age + rlnorm(n, meanlog = 0, sdlog = 0.5)
dd <- density(y, adjust = 1.5,)

hist(y, probability = T, axes=F, nclass=20, ylab=" ", xlab="", main="Positively Skewed\n Skewed to the right")
lines(dd$x, dd$y, col=2, lwd=2)
abline(v=2.27, lty=1, col=4, lwd=2)

## Negatively skewed or Skewed to the left
set.seed(191)
n <- 1000
age <- rnorm(n, 9, 0.7)
y <- 0.6+ 0.1*age - rlnorm(n, meanlog = 0, sdlog = 0.35)
dd <- density(y, adjust = 1.5)

hist(y, probability = T, axes=F, nclass=20, ylab=" ", xlab="", main="Negatively skewed\n Skewed to the left")
lines(dd$x, dd$y, col=2, lwd=2)
abline(v=0.62, lty=1, col=4, lwd=2)

## Bimodal
set.seed(191)
n <- 1000
y <- c(rnorm(0.8*n, 20, 6), rnorm(0.2*n, 80, 10))
dd <- density(y, adjust = 1.8,)

hist(y, probability = T, axes=F, nclass=20, ylab=" ", xlab="", main="Bimodal", ylim=c(0, 0.05))
lines(dd$x, dd$y, col=2, lwd=2)