Federico: You might also look at Professor Agresti's observations on exact vs approximate, which appeared in the American Statistician a few years ago. (I believe it was the AS; my memory isn't what it once was.)
Google produced this http://www.amstat.org/publications/tas/index.cfm?fuseaction=agresti1998 when searching for "approximate is better than exact" Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFax: 614-455-3265 http://www.StatisticalEngineering.com -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Spencer Graves Sent: Thursday, January 13, 2005 7:08 PM To: Uwe Ligges Cc: R-help mailing list Subject: Re: [R] Exact poisson confidence intervals "Exact confidence limits" are highly conservative. I have not studied this for the Poisson distribution, but for the binomial distribution, Brown, Cai and DasGupta (2001, 2002) showed that the exact coverage probabilities exhibit increasingly wild oscillations as the binomial probability goes to either 0 or 1. The interval width for "exact" 95% confidence intervals is increased to compensate for these oscillations so the minimum coverage is 95%. In practice, this means that the actually coverage may be much higher, possible as much as 99% or more in most applications. Moreover, unless the binomial / Poisson parameter is exactly constant, any minor variations in the parameter would move the peaks to fill the valleys, making the "exact" intervals highly conservative. As part of this work, Brown, Cai and DasGupta also showed that the actual coverage probabilities of the standard approximate confidence limits [p.bar +/-2*sqrt(p.bar*(1-p.bar)/n)] are highly biased. They described several other alternatives. It turns out that the standard asymptotic normal approximation to the logit actually performs fairly close to the best. By extension, I would expect that the standard asymptotic normal approximation for the log(PoissonRate) might perform better than other confidence intervals for the Poisson, though of course, this should be verified. At the risk of making a fool of myself, I'll continue with this exercise: If I haven't made a mistake, the Fisher information for g = log(PoissonRate) is the PoissonRate, so the approximate standard deviation for g-hat is 1/sqrt(PoissonRate). But the maximum likelihood estimate for the PoissonRate is x.bar = mean of the Poisson observations. This would suggest x.bar*exp(+/-2/sqrt(x.bar)) as an approximate 95% confidence interval for a Poisson. If someone does any checks on this, I would like to hear the results. hope this helps. spencer graves ########################### Brown, Cai and DasGupta (2001) Statistical Science, 16: 101-133 and (2002) Annals of Statistics, 30: 160-2001 ########################### Uwe Ligges wrote: > Federico Gherardini wrote: > >> Hi all, >> Is there any R function to compute exact confidence limits for a >> Poisson distribution with a given Lambda? > > > For sure you are looking for certain quantiles of the poisson > distribution? See ?Poisson. > > Uwe Ligges > > >> Thanks in advance >> Federico >> >> ______________________________________________ >> [email protected] mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide! >> http://www.R-project.org/posting-guide.html > > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
