R help - Feb 2011 - Confidence interval based on MLE

Hi there,

I have fitted a sample (with size 20) to a normal and/or logistic 
distribution using fitdistr() in MASS or fitdist() in fitdistrplus 
package. It's easy to get the parameter estimates. Now, I hope to report 
the confidence interval for those parameter estimates. However, I don't 
find a function that could give the confidence interval in R.

I hope to write a function, however, I don't find some detailed 
information on the CI based on MLE. Would you please to give me some 
hints on the CI calculation based on MLE?

Any suggestions will be really appreciated. Thanks in advance.

Regards,
Jinsong

Jinsong Zhao <jszhao <at> yeah.net> writes:
> 
> Hi there,
> 
> I have fitted a sample (with size 20) to a normal and/or logistic 
> distribution using fitdistr() in MASS or fitdist() in fitdistrplus 
> package. It's easy to get the parameter estimates. Now, I hope to
report
> the confidence interval for those parameter estimates. However, I don't
> find a function that could give the confidence interval in R.
> 
> I hope to write a function, however, I don't find some detailed 
> information on the CI based on MLE. Would you please to give me some 
> hints on the CI calculation based on MLE?
   Well, for the normal distribution I believe that the standard-error-
based confidence intervals are the same as those based on the MLE,
but in general I would suggest something along these lines:
> library(bbmle)
> z <- rnorm(20)
> m <-
mle2(z~dnorm(mean=mu,sd=sd),start=list(mu=0,sd=1),data=data.frame(z))
Warning message:
In dnorm(x, mean, sd, log) : NaNs produced
> confint(m)
Profiling...
         2.5 %   97.5 %
mu -0.07880835 0.985382
sd  0.87314467 1.633600