[R] Confidence interval based on MLE

[Jinsong Zhao]

On 2011-2-6 22:56, Ben Bolker wrote:
> 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
>

Thank you very much for your kindly help and the way to get MLE through 
bbmle package. It works well.

I have a interval related question. I have a sample data set, with size 
20 or less. And I fit it to a three parameter distribution, e.g., a 
triangular distribution (oops, it cannot fitted by mle2 :-(). I get the 
quantile, q, for a given probability, p. Then, I hope to get the 
confidence (or prediction?) interval for the quantile, q. However, I 
don't know how to do.

I refer to some books on ecological data analysis. There's a explicit 
formula for CI to the normal distribution's q, based on delta method or 
Fieller's theorem. (And I think they should work for logistic 
distribution). But I don't find any thing that for other distribution.

BTW, is it possible to get a interval of p for a given q? Although, it's 
not a normal way in the view of statistics, it has a lot applications.

Any suggestions or comments will be really appreciated. Thanks in advance.

Regards,
Jinsong