How to get the 95% confidence interval in R?

Question

I would like to find the 95% CI for the MLE for my parameter in a function but I have no idea how.

The given function is a power-law distribution with

f(x)=Cx^(-mu),

I calculated the MLE for mu using the bbmle package in R.

Some people on the internet say use profile likelihood to do it but I am not sure how to in R, or other methods which lead to the same results are fine too.

Much appreciate and thanks in advance!

Update:

load("fakedata500.Rda")
> library(stats4)
> library(bbmle)
> x<-fakedata500
> pl <- function(u){-length(x)*log(u-1)-length(x)*(u-1)*log(min(x))+u*sum(log(x))}

mle1<-mle2(pl, start=list(u=2), data=list(x))
> summary(mle1)
Maximum likelihood estimation

Call:
mle2(minuslogl = pl, start = list(u = 2), data = list(x))

Coefficients:
Estimate Std. Error z value     Pr(z)    
u  2.00510    0.04495  44.608 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

-2 log L: 1300.166 

So the estimated mu is 2.00510 and I would like to get the 95% CI of it, it might look nonsense since my started mu was 2 so 2.00510 is very close to it, but I am going to apply this method to other data sets too which I havn't come across yet so really hope to find a way to do it.

Answer 1

(Converted from a comment.)

If you're using mle2 from the bbmle package you should just be able to say confint(mle1) to get the 95% profile confidence intervals. See ?confint.mle2, or try vignette("mle2",package="bbmle") and search for "confint" for more information.