minfnormalconf=function(x,y){

#this will spit out the quantiles of the MI estimated using
# a bivariate normal PDF for the bootstrap samples..

library(mvtnorm)
library(akima)

air3  = cbind(x,y)
x=air3[,1]
y=air3[,2]

result.12 = dmvnorm(air3, mean=colMeans(air3), sigma=var(air3))
result.1=dnorm(x,mean=mean(x), sd=sd(x))
result.2=dnorm(y,mean=mean(y), sd=sd(y))

#Average Mutual Information .. Moon et al. (1995)
tobs = sum(result.12 * log2(result.12 /(result.1 * result.2)))
print(c(tobs))

n=length(x)

#500 bootstrap samples..
nsim   = 500

#vector of MI for the bootstrap samples..
simval = rep(0,nsim)

#vector of correlations of the bootstrap samples..
simcor=rep(0,nsim)

for (i in 1:nsim) {

#sample y but not x. This disturbs the joint occurrence of x and y
# you can do the other way as well..

xy=sample(y,replace=TRUE)
samp = cbind(y1 = x, y2 = xy)	
x1=samp[,1]
y1=samp[,2]

#to obtain confidence interval of MI both x and y are undisturbed.
#xn=sample(1:n, replace=TRUE)
#   samp = cbind(y1 = x[xn], y2 = y[xn])	

result.12 = dmvnorm(samp, mean=colMeans(samp), sigma=var(samp))
result.1=dnorm(x1,mean=mean(x1), sd=sd(x1))
result.2=dnorm(y1,mean=mean(y1), sd=sd(y1))

#Average Mutual Information .. Moon et al. (1995)
simval[i] = sum(result.12 * log2(result.12 /(result.1 * result.2)))


#Correlation
simcor[i]=cor(samp[,1],samp[,2])
   }

quantile(simval,c(0.05,0.1,.50,.90,.95))
quantile(simcor,c(0.05,0.1,.50,.90,.95))

par(mfrow=c(1,2))

zz=myboxplot(simcor,ylim=range(simcor,cor(x,y)),xlab="",ylab="Cor",plot=F)
zz$names=rep("",length(zz$names))
z1=bxp(zz,xlab="",ylab="Cor",ylim=range(simcor,cor(x,y)), cex=1.25)
points(z1, cor(x,y),cex=1.5,pch=16)
title(main="Boxplot of bootstrap correlations")

zz=myboxplot(simval,ylim=range(simval,tobs),xlab="",ylab="MI",plot=F)
zz$names=rep("",length(zz$names))
z1=bxp(zz,xlab="",ylab="MI",ylim=range(simval,tobs),cex=1.25)
points(z1, tobs,cex=1.5,pch=16)
title(main="Boxplot of bootstrap MI from Normal PDFs")

}