Re: [R] Confidence limits for the parameter of the Poisson distribution

From: Rolf Turner <r.turner_at_auckland.ac.nz>
Date: Fri, 07 Nov 2008 10:14:32 +1300

On 7/11/2008, at 9:26 AM, Hoang Trong Minh Tuan wrote:

> Hi all,
> So far I only know one way to get the confidence limit for the
> Poisson
> distribution is to use the look-up table given by the 2 parameter (the
> number of observation x and the confidence level, e.g. 95%) and the
> table is
> limit by the maximum number of observations (x <= 50).
> I know the formula to compute the CI, however, mathematically it
> is not
> easy to do it. So, anyone know an R function to do this. Thanks
>
> Tuan.

You may find the URL

        http://www.math.mcmaster.ca/peter/s743/poissonalpha.html

useful.

        cheers,

                Rolf Turner

P.S. The foregoing URL discusses the issues in terms of a *single* observation. Note that if X_1, ..., X_n are i.i.d. Poisson(lambda) then Y = X_1 + ... + X_n is Poisson(n*lambda).

Note that the ``exact'' confidence limits are very conservative.

                R. T.

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