findUL <- function(step = 0.01, initStep = 0, fun, MLE, level = 3.84, ...)
{
value <- 0
step1 <- step

Lbeta <- MLE - initStep
while (value < level) {
Lbeta <- Lbeta - step1
value <- fun(Lbeta, ...)$"-2LLR"
}
Lbeta0 <- Lbeta
Lbeta1 <- Lbeta + step1
tempfun <- function(beta){
return( level - fun(beta, ...)$"-2LLR" )
}
temp1 <- uniroot(tempfun, lower=Lbeta0, upper=Lbeta1)
Lbeta <- temp1$root
value1 <- level - temp1$f.root
value <- 0
Ubeta <- MLE + initStep
while (value < level) {
Ubeta <- Ubeta + step
value <- fun(Ubeta, ...)$"-2LLR"
}
Ubeta0 <- Ubeta
Ubeta1 <- Ubeta - step
temp2 <- uniroot(tempfun, lower=Ubeta1, upper=Ubeta0)
Ubeta <- temp2$root
value <- level - temp2$f.root
return(list(Low = Lbeta, Up = Ubeta, FstepL=temp1$estim.prec,
FstepU =temp2$estim.prec, Lvalue = value1, Uvalue = value))
}