#####################################################
# R codes for profiling the PEL confidence interval #
# a: value of 1-alpha (0.95 for 95% CI)             #
# YEL: Maximum PEL estimator of Ybar                #
# ys: vector of sampled y_i's                       #
# nss: effective sample size                        #
#                                                   #
# (No auxiliary information is used!)               #
#                                                   #
# Written by Changbao Wu, March, 2000               #                                  
#####################################################
tol<-1e-08
cut<-qchisq(a,1)
#------------
t1<-YEL
t2<-max(ys) 
dif<-t2-t1
while(dif>tol){
      tau<-(t1+t2)/2
      M<-Lag1(ys,ds,tau)
      elratio<-2*nss*sum(ds*log(1+M*(ys-tau)))
      if(elratio>cut) t2<-tau
      if(elratio<=cut) t1<-tau
      dif<-t2-t1
            }
UB<-(t1+t2)/2
#------------
t1<-YEL
t2<-min(ys) 
dif<-t1-t2
while(dif>tol){
      tau<-(t1+t2)/2
      M<-Lag1(ys,ds,tau)
      elratio<-2*nss*sum(ds*log(1+M*(ys-tau)))
      if(elratio>cut) t2<-tau
      if(elratio<=cut) t1<-tau
      dif<-t1-t2
            }
LB<-(t1+t2)/2