# ----------------------------------------------
# Program: Transformations1.S  
#  Author: Steven M. Boker
#    Date: Thu Sep 30 10:18:51 EST 2004
#
# Examples of transformations 
#
# ----------------------------------------------

# ----------------------------------------------
#  Create four example distributions

x1 <- rnorm(300, mean=0, sd=1)
x2 <- rexp(300)
x3 <- (1 / rnorm(300, mean=1, sd=.1))
x4 <- rnorm(300, mean=1, sd=.2)^4

# ----------------------------------------------
#   Boxplots for the distributions

graphsheet(height=6.4,width=6.4)
par(mfrow=c(2,2))
boxplot(x1, xlab="x1")
boxplot(x2, xlab="x2")
boxplot(x3, xlab="x3")
boxplot(x4, xlab="x4")

# ----------------------------------------------
#  Histograms for the distributions

graphsheet(height=6.4,width=6.4)
par(mfrow=c(2,2))
hist(x1, xlab="x1")
hist(x2, xlab="x2")
hist(x3, xlab="x3")
hist(x4, xlab="x4")

# ----------------------------------------------
#  Quantile-Normal plots for the distributions

graphsheet(height=6.4,width=6.4)
qqmath(~ x1, 
         distribution=qnorm,
         prepanel = prepanel.qqmathline, 
	 panel = function(x, y) {
	   panel.qqmathline(y, distribution = qnorm)
	   panel.qqmath(x, y)
	 },
         aspect=1,
         xlab = "Normal Distribution",
         ylab="x1")

graphsheet(height=6.4,width=6.4)
qqmath(~ x2, 
         distribution=qnorm,
         prepanel = prepanel.qqmathline, 
	 panel = function(x, y) {
	   panel.qqmathline(y, distribution = qnorm)
	   panel.qqmath(x, y)
	 },
         aspect=1,
         xlab = "Normal Distribution",
         ylab="x2")

graphsheet(height=6.4,width=6.4)
qqmath(~ x3, 
         distribution=qnorm,
         prepanel = prepanel.qqmathline, 
	 panel = function(x, y) {
	   panel.qqmathline(y, distribution = qnorm)
	   panel.qqmath(x, y)
	 },
         aspect=1,
         xlab = "Normal Distribution",
         ylab="x3")

graphsheet(height=6.4,width=6.4)
qqmath(~ x4, 
         distribution=qnorm,
         prepanel = prepanel.qqmathline, 
	 panel = function(x, y) {
	   panel.qqmathline(y, distribution = qnorm)
	   panel.qqmath(x, y)
	 },
         aspect=1,
         xlab = "Normal Distribution",
         ylab="x4")

# ----------------------------------------------
#  Testing Positive Exponents using Quantile-Normal plots

tlen <- length(x4)
exponent <- c(rep(1/4, tlen), rep(1/3, tlen), rep(1/2, tlen),
              rep(1, tlen),  rep(2, tlen), rep(3, tlen))
tempx2 <- c(x4^(1/4), x4^(1/3), x4^(1/2), x4^1, x4^2, x4^3)
graphsheet(height=6.4,width=8)
qqmath(~ tempx2 | as.factor(exponent), 
	prepanel = prepanel.qqmathline, 
	panel = function(x, y) {
	    panel.qqmathline(y, distribution = qnorm)
	    panel.qqmath(x, y)
	},
	aspect=1, layout=c(3,2),
	xlab = "Unit Normal Quantiles",
	ylab = "x4")


# ----------------------------------------------
#  Testing Negative Exponents using Quantile-Normal plots

tlen <- length(x4)
exponent <- c(rep(-1/3, tlen), rep(-1/2, tlen),
              rep(-1, tlen),  rep(-2, tlen))
tempx2 <- c(x3^(-1/3), x3^(-1/2), x3^-1, x3^-2)
graphsheet(height=6.4,width=8)
qqmath(~ tempx2 | as.factor(exponent), 
	prepanel = prepanel.qqmathline, 
	panel = function(x, y) {
	    panel.qqmathline(y, distribution = qnorm)
	    panel.qqmath(x, y)
	},
	aspect=1, layout=c(2,2),
	xlab = "Unit Normal Quantiles",
	ylab = "x3")