##################################################################
### Section 9.4.1: Misconceptions of correlation and dependence
##################################################################

# Generate Fig 9.11

# Note that the scale parameter of the Gamma distribution in R corresponds to 1/scale as defined in the book 

# Functions

rclcop<-function(n,d,theta)
{
gammavals<-rgamma(n,1/theta) 
result<-matrix(1,d,n)
for(i in (1:n))
{
result[,i]<--log(runif(d))/gammavals[i]
result[,i]<-(result[,i]+1)^(-1/theta)
}
result
}

# Program

library(MASS)
N<-2000
# Upper left
ULvals<-mvrnorm(N,c(0,0),matrix(c(1,0.5,0.5,1),2,2))
# Lower left
Uvals<-pnorm(ULvals)
LLvals<-qgamma(Uvals,3,1)
# Upper right
Uvals<-rclcop(2000,2,1)
URvals<-qnorm(Uvals)
# Lower right
LRvals<-qgamma(1-Uvals,3,1)

plot(ULvals,xlab="",ylab="")
plot(t(URvals),xlab="",ylab="")
plot(LLvals,xlab="",ylab="")
plot(LRvals,xlab="",ylab="")