Dear all,
Can anyone take a look at my program below?
There are two functions: f1 (lambda,z,p1) and f2(p1,cl, cu).
I fixed p1=0.15 for both functions. For any fixed value of lambda (between
0.01 and 0.99),
I solve f1(p1=0.15, lambda=lambda, z)=0 for the corresponding cl and cu
values.
Then I plug the calculated cl and cu back into the function f2.
Eventually, I want to find the lambda value and the corresponding cl and cu
values that would
make f2=0.1.
The result of this program does not seem to match the answer I have. Can
some one give me
some hint? Thank you very much.
Hannah
u1 <- -3
u2 <- 4
f1 <- function(lambda,z,p1){
lambda*(p1*exp(u1*z-u1^2/2)+(0.2-p1)*exp(u2*z-u2^2/2))-(1-lambda)*0.8}
f2 <- function(p1,cl, cu){
0.8*(pnorm(cl)+(1-pnorm(cu)))/(0.8*(pnorm(cl)+(1-pnorm(cu)))+p1*(pnorm(cl-
u1)+(1-pnorm(cu-u1)))+(0.2-p1)*(pnorm(cl-u2)+(1-pnorm(cu-u2))))}
p1 <- 0.15
lam <- seq(0.01,0.99, by=0.001)
x1 <- numeric(length(lam))
for (i in 1:length(lam)){
cl <- uniroot(f1, lower =-10, upper = 0,
tol = 1e-10,p1=p1,lambda=lam[i])$root
cu <- uniroot(f1, lower =0, upper = 10,
tol = 1e-10,p1=p1,lambda=lam[i])$root
x1[i]<- f2(p1=p1, cl=cl, cu=cu) }
k <- 1
while(k<length(lam) && x1[k]<=0.1){
k=k+1
}
k<-k-1;k
lower <- uniroot(f1, lower =-10, upper = 0,
tol = 1e-10,p1=p1,lambda=lam[k])$root
upper <- uniroot(f1, lower =0, upper = 10,
tol = 1e-10,p1=p1,lambda=lam[k])$root
res <- c(lower, upper)
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