bbmedci<-function(x,conflevel=0.95,nboots=120){
#This function will calculate the "basic bootstrap"#
#  confidence interval for the population median. #
#nboots = B = number of bootstrap samples to take#
#tstar will contain the median calculated for each bootstrap#
#  sample #
alpha<-1-conflevel
tstar<-rep(0,nboots)
for (b in 1:nboots){
  tstar[b]<-median(sample(x,replace=T))
}
tstar<-sort(tstar)
mtstar<-mean(tstar)
biasest<-mtstar-median(x)
lowtstar<-0.5*(tstar[floor(nboots*alpha/2)]+tstar[ceiling(nboots*alpha/2)])
hitstar<-0.5*(tstar[floor(nboots*(1-alpha/2))]+tstar[ceiling(nboots*(1-alpha/2))])
ucl<-median(x)-(lowtstar-median(x))
lcl<-median(x)-(hitstar-median(x))
c(lcl,ucl)
}


stbmedci<-function(x,conflevel=0.95,nboots=120){
#This function will calculate the "studentized bootstrap"#
#  confidence interval for the population median. #
#It uses the simple variance estimate and so should agree#
#  with the basic bootstrap except for the bias correction.#
#nboots = B = number of bootstrap samples to take#
#tstar will contain the median calculated for each bootstrap#
#  sample #
#This version has the zstars in the right order.#
alpha<-1-conflevel
tstar<-rep(0,nboots)
for (b in 1:nboots){
  tstar[b]<-median(sample(x,replace=T))
}
tstar<-sort(tstar)
mtstar<-mean(tstar)
vtstar<-var(tstar)
biasest<-mtstar-median(x)
zstar<-(tstar-median(x))/sqrt(vtstar)
lowzstar<-0.5*(zstar[floor(nboots*alpha/2)]+zstar[ceiling(nboots*alpha/2)])
hizstar<-0.5*(zstar[floor(nboots*(1-alpha/2))]+zstar[ceiling(nboots*(1-alpha/2))])
lcl<-(median(x)-biasest)-hizstar*sqrt(vtstar)
ucl<-(median(x)-biasest)-lowzstar*sqrt(vtstar)
c(lcl,ucl)
}