#
#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

# fix the random.seed, so I'll always get the same answer:
set.seed(10131985)

mu = 1.0
beta = 2.0

Nsim = 10^4
U = runif(Nsim)
X = mu - beta * log( 1/U - 1 )
Y = rlogis(Nsim,location=mu,scale=beta)

###postscript("../../WriteUp/Graphics/Chapter2/ex_2_2_logistic.eps", onefile=FALSE, horizontal=FALSE)

par(mfrow=c(1,2))
hist(X,freq=F,main="Logistic from Uniform",breaks=100)
hist(Y,freq=F,main="Logistic from R(rlogis)",breaks=100)

###dev.off()

mu = 1
sigma = 2

Nsim = 10^6
U = runif(Nsim)
X = mu + sigma * tan( pi * (U-0.5) )
Y = rcauchy(Nsim,location=mu,scale=sigma)

range = as.double( quantile( c(X,Y), probs=c(0.05,0.95) ) )
allMin = min( min(X),min(Y) )
allMax = max( max(X),max(Y) )
brks = seq(range[1],range[2],length.out=100)

par(mfrow=c(1,2))
hist(X,freq=F,main="Cauchy from Uniform")
hist(Y,freq=F,main="Cauchy from R(rcauchy)")