# R program to produce probability plots and density probability plots.
# Random variables from standard normal and t distributions are simulated
# and plotted.
#
# Density probability plots are described in Jones M.C. 2004.  The American
# Statistician 58:176–177.

n=1000
z=sort(rnorm(n))           # Simulated standard normal random variables.
t=sort(rt(n,5))            # Simulated t random variables.
zn=qnorm(((1:n)-.5)/n)     # Normal scores.
fn=exp(-zn*zn/2)/sqrt(pi)  # Normal pdf evaluated at normal scores.

zval=seq(-3,3,.05)
fzval=exp(-zval*zval/2)/sqrt(pi)

layout(matrix(c(1,2,3,4),2,2,byrow=TRUE))

# Probability plot of simulated normal variables.
plot(z,zn,xlab="z",ylab="normal scores")

# Density probability plot of simulated normal variables.
plot(z,fn,xlab="z",ylab="density",type="p",pch=1,
   xlim=c(-4,4))
points(zval,fzval,type="l")

# Probability plot of simulated t variables.
plot(t,zn,xlab="t",ylab="normal scores")

# Density probability plot of simulated t variables.
plot(t,fn,xlab="t",ylab="density",type="p",pch=1,
   xlim=c(-4,4))
points(zval,fzval,type="l")